wave motion

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AAddvvaanncceedd PPhhyyssiiccss 11998800--11999999 ( Section B: Wave Motion )

物物理理學學人人 hhttttpp::////ccoommee..ttoo//pphhyyssiicciisstt AAddvvaanncceedd PP hhyyssiiccss 11998800--11999999

Content

Section B: Wave Motion Content Page

PART 1: MC

1. Wave Propagation

2. Wave Phenomenon

3. Electromagnetic Spectrum

4. Stationary Wave

5. Acoustics

6. Optical Instrument

PART 2: Structure Type Question

1. Wave Phenomenon - Interference

2. Wave Phenomenon – Diffraction Grating

3. Wave Phenomenon - Polarisation

4. Stationary Wave

5. Acoustics


PART3: Essay Type Question

1. Wave Propagation, Wave Phenomenon

2. Stationary Wave

3. Acoustics


PART4: Appendix

MC answers

Useful Formulae in Advanced Level Physics

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物物理理學學人人 hhttttpp::////ccoommee..ttoo//pphhyyssiicciisstt AAdd vv aanncceedd PPhhyyssiiccss 11998800--11999999

Section B : Wave Motion (1. Wave Propagation − M.C.) P.1

1. WAVE PROPAGRATION 1980−I−18

The displacement y of a point P on a plucked string varies with time t as shown in the graph above. Which of the following correctly shows the variation of the velocity v of the point P with time ? A. B.

C. D.

E.

1986−I−28

Two waveforms X and Y are displayed on a C.R.O. screen. Which of the following statements is correct ? A. X leads Y by a phase difference of π/4. B. X leads Y by a phase difference of π/2. C. Y leads X by a phase difference of π/4. D. Y leads X by a phase difference of π/2. E. There is no phase difference between X and Y.



1987−I−18 A stroboscope is used to freeze a wave pattern. When the flashing frequency of the stroboscope is slightly reduced, the wave pattern appears to A. move forward. B. move backward. C. move forward and then backward. D. move backward and then forward. E. remain stationary. 1988−I−25

A loudspeaker at O produces a progressive sound wave of frequency 330 Hz which propagates along OA with a speed of 330 m/s. The phase difference between the air vibrations at P and Q, 0.5 m apart, is A. dependent on the distance OP. B. zero. C. 0.5 radians. D. π/2 radians. E. π radians. 1989−I−20 A rotating disc, with a small hole near its edge is illuminated by a lamp which flashes at a rate of 50 times per second. The hole is observed to be moving backwards slowly relative to the actual direction of rotation of the disc. The disc is probably rotating at A. 24 revolutions per second B. 26 revolutions per second C. 50 revolutions per second D. 98 revolutions per second E. 102 revolutions per second 1990−I−15 (For AL only) A rubber band is of unstretched length l and force constant k. When it is stretched to a length 2 l, the speed of transverse waves on it is v. What will be the speed of transverse waves when it is stretched to a length 3 l ?

A. v B. 2 v C. 3v /2 D. 3 v E. 2 v 1990−I−17

A disc with a spot on it rotates at a constant sped in a darkened room. a student shines a stroboscopic lamp on it. When the flashing rate is 8 flashes per second, the disc appears stationary with two spots on it as shown. When the flashing rte is reduced to 2 flashes per second, the disc would appear to be stationary with A. no spot B. one spot C. two spots

D. four spots E. eight spots



1990−I−21

A boat travels in shallow water, in which waves of all wavelengths travel at a speed of 4.0 m/s. What is the

speed of the boat if the bow wave generated by the boat has an apex angle of 30o ? A. 2.0 m/s B. 2.3 m/s C. 4.0 m/s D. 6.9 m/s E. 8.0 m/s 1991−I−25

Two trains of traveling waves W1 and W2, of the same amplitude, wavelength and speed move in opposite directions. The period of both of the waves is T and their amplitude is A. At time t = t1, the waves W1 and W2 are as shown in the figure above. Which of the following statements is/are correct ?

(1) The wavelength of the waves is four times the distance MN. (2) At time t = t1 + T/4, the displacement at point M is 2A. (3) Point N is a displacement node.

A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1992−I−20

Figure (a) shows the positions of equally spaced molecules in a solid lattice. A longitudinal sond wave travels from left to right through the solid. At a certain instant, the displaced positions of the molecules are shown in Figure (b). Immediately afterwards, what will be the directions of motion of particle 1 and particle 7 ?

Particle 1 Particle 7 A. to the right to the right B. to the right to the left C. to the left to the right D. to the left to the left E. at rest at rest



1993−I−24

. A displacement-time graph of a particle in a plane progressive wave is shown above. What is the frequency of this wave ? A. 1.43 Hz B. 2 Hz C. 2.22 Hz D. 4 Hz E. 5 Hz 1994−IIA−14(AL)/ 1994−IIA−9(AS)

Figure (a) represents the displacement-position graph of a travelling wave at a certain instant and Figure (b) represents the displacement-time graph of a particle in the wave. The speed of the wave is A. 300 m/s B. 150 m/s C. 1.2 m/s D. 0.6 m/s E. 0.3 m/s 1995−IIA−12(AL)/ 1995−IIA−7(AS)

The figure shows a sound wave travelling to the right in air. Air particles A and B are at the centre of a compression and a rarefaction respectively. Which of the following gives correctly the directions of motion of A and B at the moment shown ? Particle A Particle B A. to the right to the left B. to the right at rest C. to the right to the right D. at rest to the right E. to the left to the right 1996−IIA−11(AL)

The least separation between two points with a phase difference of π/6 on a progressive wave is 0.05 m. If the velocity of the wave is 150 m/s, the frequency of the wave is A. 125 Hz. B. 250 Hz C. 375 Hz D. 500 Hz E. 1000 Hz



1997−IIA−11(AL)

The above figure shows a transverse wave propagating to the right along a string. At the moment shown, which of the labelled particles has its velocity and acceleration in opposite directions?

A. P B. Q C. R D. S E. T

1998−IIA−11(AL)

The displacement-time graphs of two oscillating particles P and Q are shown below.

Which of the following phase relations between P and Q is correct? A. P leads Q by π/4 B. leads Q by π/2 C. P leads Q by

π D. Q leads P by π/4 E. Q leads P by π/2 1998−IIA−13(AL)

The above figure shows a transverse wave propagating along a string. At the instant shown, the

particle D on the string is moving downward. Which of the following deduction is/are correct? (1) The wave is propagating to the left. (2) Particle B takes longer than particle A to return for the first time to the respective equilibrium

positions along the dotted line. (3) Particles C and D are moving in opposite directions at the instant shown. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)


Section B : Wave Motion (2. Wave Phenomenon − M.C.) P.6

2. WAVE PHENOMENA 1980−I−42 / 1984−I−47 Which of the following statements about wave motion is correct ? (1) Diffraction cannot be exhibited by longitudinal waves. (2) Refraction prevents the formation shadows with perfectly sharp edges. (3) Reflection is sometimes accompanied by a phase change of radians. A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct 1996−IIA−17(AL)

Which of the following statement is/are correct? (1) Radio waves can be polarized (2) Ultrasonic waves are electromagnetic wave in nature (3) All standing waves are transverse waves A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)



<< Reflection >> 1987−I−19

A wave pulse is moving with uniform speed along a rope attached to a fixed wall. A graph of the vertical displacement s against time t for a point P on the rope would be :



1990−I−23 ( Reflection & Superposition )

The figure shows two pulses travelling to the right along a rope. The right-hand end of the rope is fixed to a wall. The following figures represent predicted positions of the pulses at later times (where appropriate, the arrows indicate the direction of a pulse). Which of the following could NOT arise from the initial given condition ?

A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1998−IIA−12(AL)

Three identical long spiral springs are connected respectively to a wall, a light thread and a heavy spring. If a crest-shaped pulse is sent along each spiral spring towards the respective boundary, which of the following diagrams correctly show(s) the reflected pulse ? (Transmitted pulse is not shown)

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) << Refraction >>



1983−I−37

Light travels in media M1 and M2 with speeds v1 and v2 respectively. When light travelling from medium

M1 strikes a boundary between the two media with angle of incidence i, it suffers total internal reflection.

This indicates that (1) v1 is less than v2.

(2) sin i is less than v1/v2.

(3) sin i is greater than v2/v1.

A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct 1985−I−17

A beam of ultrasound is being emitted from a submarine under water towards the water surface. Which of the following statements is true ? A. The refracted beam leaving the surface will bend away from the normal. B. The refracted beam will bend towards the normal. C. The refracted beam will travel in the same direction as the incident beam. D. Total internal reflection will occur. E. The refracted beam will travel along the water surface. 1984−I−46



Light travels between two media X and Y. If the refractive index of X is greater than the refractive index of Y, which of the following is/are possible ray diagram(s) ?

A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct 1986−I−21

A glass vessel in the shape of a triangular prism is filled with water, and light is incident normally on the face XY. If the refractive indices for water and glass are 4/3 and 3/2 respectively, total internal reflection will occur at the glass-air surface XZ only for sin q greater than A. 1/2 B. 2/3 C. 3/4 D. 8/9 E. 16/27 1990−I−16.

The figure shows wave crests moving in the direction of the arrow towards the interface PQ between a shallow region and a deep region as shown in the figure above. Which of the lines may represent one of the wave crests in the deep region ? A. I B. II C. III D. IV E. V 1994−IIA−15(AL)/ 1994−IIA−10(AS)



The speed of light in a certain material is 1.6 x 108 m/s. Find the critical angle for the material and air.

(Speed of light in air = 3 x 108 m/s)

A. 28.1o B. 32.2o C. 41.8o D. 48.0o E.

57.8o

1995−IIA−14(AL)/1995−IIA−8(AS) In Young's double-slit experiment, which of the following combinations of monochromatic light, the slit-separation and the slit-to-screen distance would produce the widest fringe separation on the screen ? Monochromatic light Slit-separation Slit-to-screen distance A. red light 1 mm 1 m B. red light 1 mm 2 m C. red light 2 mm 1 m D. green light 1 mm 2 m E. green light 2 mm 2 m 1995−IIA−13(AL)

When a beam of light travels from a medium X to another medium Y, the variation in intensity of the refracted beam when angle θvaries from 0o to 90o is as shown. what is the ratio speed of light in X

speed of light in Y ?

A. 1 : 2 B. 1 : 3 C. 2 : 1 D. 2 : 3 E. 3 : 1 1997−IIA−13(AL) A beam of monochromatic light passes through three media of refractive indexes n1, n2 and n3 respectively as shown. The boundaries between the media are parallel.

Which of the following relations between n1, n2 and n3 is correct? A. n1> n3 > n2 B. n3> n1 > n2 C. n1> n2 > n3 D. n2> n1 > n3 E. n3> n2 > n1



1998−IIA−14(AL)

A wave is incident on a boundary between two media X and Y at an angle of incidence i. AB

represents the incident wavefront and CD the refracted wavefront. Which of the following statements is/are correct?

(1) The frequency of the wave changes when passing from X to Y. (2) The end B of the wavefront travels to D at the same time as the end of travels to C. (3) When angle i increases, it is possible for the wavefront to be totally reflected at the boundary. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)

1996−IIA−12(AL)

When monochromatic light travels from glass to air, the emergent light, relative to the incident light, shows an increase in (1) frequency (2) wavelength (3) velocity

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)

<< Polarisation >> (For AL only)



1984−I−14

Three polaroid sheets are arranged in the three different ways as shown above Figure 1, 2 and 3 and an observer looks towards the light source as shown in the diagrams. The bold lines indicate the directions of the transmission axes in each case. Which of the following statements correctly describes the effect of the combination ? Figure 1 Figure 2 Figure 3 A. opaque opaque opaque B. opaque opaque transparent C. opaque transparent opaque D. opaque transparent transparent E. transparent opaque transparent 1985−I−20 When parallel light is incident at the Brewster angle in air on the surface of a glass block, A. the light is totally reflected. B. the reflected light is partially polarised. C. the transmitted light is unpolarised. D. the reflected and refracted wavefronts are at right angles to each other. E. the angle of incidence is equal to the angle of refraction. 1987−I−23

An unpolarised microwave travels along the positive y-axis. A metal grid is placed in the xz-plane. The electromagnetic wave detected by the detector is A. of zero intensity. B. unpolarised. C. plane-polarised in the yz-plane. D. plane-polarised in the xz-plane. E. plane-polarised in the xy-plane.



1986−I−23 When a beam of unpolarised light travelling in air falls on the surface of a block of glass, it is possible to find an angle of incidence such that A. none of the light is reflected. B. all of the light is reflected. C. the reflected light is completely plane polarised. D. the transmitted light is completely plane polarised. E. the reflected light and transmitted light are both completely plane polarised. 1988−I−24

Polarized light is obtained by passing a narrow beam of unpolarized light from source S through a tank of water to which a drop of milk has been added. Which of the following statements is/are correct ? (1) Light from source S must be monochromatic. (2) Completely polarized light is detected at position M. (3) The drop of milk provides particles to scatter the light. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1990−I−25 When parallel light is incident at the Brewster angle in air on the surface of a glass block, which of the following statements is/are correct ? (1) The refracted light is plane-polarised. (2) The reflected light is plane-polarised. (3) The reflected ray and the refracted ray are at right angles to each other. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1991−I−23



Light from an unpolarised source is allowed to fall on a piece of polaroid P and then on a second polaroid A. In the position shown in the diagram, the intensity of the light emerging from polaroid A is a maximum. As A is slowly rotated, the intensity of light emerging is reduced to half the maximum value at angle θ1 and to a minimum at angle θ2 . Which of the following gives the correct values of angles θ1 and θ2 ? θ1 θ2 A. 30o 90o B. 45o 90o C. 45o 180o D. 60o 90o E. 60o 180o 1992−I−24 When unpolarised light travelling in air falls on the surface of a glass block, it is possible to find an angle of incidence such that A. none of the light is reflected. B. the reflected light and the transmitted light are both plane polarised. C. all the light is reflected. D. the transmitted light is plane polarised. E. the reflected light is plane polarised. 1992−I−25

A light source S is viewed through two parallel pieces of polaroid P and Q. Q is gradually rotated until the field of view becomes dark. Which of the following conclusions can be drawn ? (1) The experiment shows that light is a transverse wave. (2) The experiment shows that light from source S must be unpolarised. (3) When Q is rotated further by 90o , the field of view becomes dark again. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1993−I−22



Which of the following equations correctly gives the relation between the polarising angle i and the refractive index of a material ? A. sin i = n B. n sin i = 1 C. cos i = n

D. n tan i = 1 E. tan i = n 1994−I−17 Which of the following waves can be polarised ? (1) microwaves (2) X-rays (3) ultrasonic waves A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) 1996−IIA−13(AL) When a beam of unpolarized light travelling in air falls on a water surface, it is possible to find an angle of incidence such that (1) all the light is reflected (2) the light passing into water is plane polarised (3) the reflected light is plane polarised. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) 1998−IIA−15(AL) Sunlight is scattered by air molecules in the atmosphere. Which of the following statements concerning this process is/are correct? (1) Light is absorbed by air molecules and is then re-emitted. (2) The scattered light observed on the earth’s surface is partially plane-polarised. (3) Red light is scattered more than blue light is.


<< Superposition >>



1990−I−19 The intensity of a sound wave is proportional to the square of the amplitude of the wave. If two waves of the same frequency are superimposed in phase, the total intensity is proportional to A. the mean value of the intensities of the two waves. B. the square of the sum of the two amplitudes. C. the square of the mean value of the two amplitudes. D. the square of the difference of the two amplitudes. E. the sum of the intensities of the two waves. << Beats >> (For AL only) 1981−AL−11 When two notes of nearly equal frequencies f1 and f2, with f2 > f1, are sounded together, beats are heard. Beats are periodic variations in A. pitch, with beat frequency (f2 − f1 ). B. pitch, with beat frequency 0.5(f2 + f1 ). C. loudness, with beat frequency (f2 − f1 ). D. intensity, with beat frequency 0.5(f2 − f1 ). E. intensity, with beat frequency 0.5(f2 + f1 ). 1985−AL−16 Two signal generators are connected to display the formation of beats on a C.R.O. screen. For one particular setting of the two signal generators, the following pattern is observed on the C.R.O :

If the C.R.O. time base is set at 0.2 ms cm-1, the beat frequency is A. 100 Hz B. 200 Hz C. 400 Hz D. 1000 Hz E. 2000 Hz 1986−I−25 Two stretched wires are turned to vibrate transversely at the same frequency of 1200 Hz. When the tension in one of the wires is reduced by 1 %, beats are heard as both wires vibrate. The beat frequency is A. 3Hz B. 6 Hz C. 12 Hz D. 24 Hz E. 1188 Hz 1994−I−16



Three tuning forks X, Y and Z are of slightly different frequencies. If X and Y are sounded together, 3 beats per second are heard while X and Z sounded together give 1 beat per second. Which of the following is/are correct deduction(s) ? (1) 4 beats per second are heard when Y and Z are sounded together. (2) The frequency of Z is higher than that of Y. (3) If X has the highest frequency, then the frequency of Y must be the lowest. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) << Diffraction Grating>>



1982−I−17 A diffraction grating ruled with 5000 lines per cm is illuminated normally by white light. If the wavelengths for yellow light and violet light are 600 nm and 400 nm respectively, which of the following statements is false ?

A. The central image is white. B. The violet end of the first-order spectrum is closer to the central image than is the red end of

the first-order spectrum. C. The second-order image of yellow light coincides with the third-order image of violet light. D. The angular displacement of the second-order image of yellow light from the central image is

sin-1 0.6. E. There is no fourth-order image for violet light.

1985−I−14 White light is directed normally onto a diffraction grating and the diffracted light is observed through the telescope of a spectrometer. The appearance of the zeroth order and the first order diffraction pattern will look like :

(W : white R : red B : blue) 1989−I−22



Light of wavelength l is incident normally on a diffraction grating with p lines per millimetre. The second-order diffraction maximum is at an angle q from the central position. For a second grating with 3p lines per millimetre illuminated normally by light of wavelength 5l/4, the angle between the first-order diffraction maximum and the central position is f. Which of the following relations is correct ? A. sin f = (5 sin q)/12 B. sin f = sin (5q/12) C. sinf= sin (15q)/4) D. sin f = (15 sin q)/8 E. sin f = sin (15q/8) 1991−I−21

In experiments with optical diffraction gratings, the grating spacing

wavelength of light is of the order of

A. 10-6 B. 10-3 C. 1 D. 103 E. 106 1991−I−24 When a diffraction grating is replacing by another with more lines per nm, which of the following quantities is/are increased ? (1) the angle of diffraction for every spectral line. (2) the angular separation of red and blue lines in the first order spectrum (3) the number of orders which can be observed A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1997−IIA−19(AL) A plane transmission gratin is placed at the centre of a circular 0° - 360° protractor. A beam of monochromatic light is incident normally on the grating. The zeroth-order maximum occurs at a scale reading of 90° and a first-order maximum occurs at a scale reading of 65°. At what scale reading would a second-order maximum be observed? A. 148° B. 140° C. 130° D. 58° E. 40°



1998−IIA−12(AL) A beam of red(R) light and violet (V) light strikes normally on a diffraction grating. Several orders of diffraction of the light beam are produced on each side of the central axis. The wavelength of the red light is 700 nm and that of violet light is 400 nm. How will the second- and third- order diffracted beams of both colours appear? (The central axis is marked with a dot and the diffracted beams of others orders are not shown.)

1996−IIA−15(AL)

A beam of white light is shone normally on a diffraction grating. The diagram shows the spectra of the first two orders, which may not be drawn to scale. The first-order spectrum starts at an angle of 20° from the zeroth order. The respective angular separations between the two ends (red and violet) of a spectrum are α and β for the first- and second- order spectra. Which of the following statements is/are correct? (1) In the first-order spectrum, P is the violet end (2) β is greater than α (3) There is no third-order spectrum A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)



<< Diffraction >> (For AL only) 1985−I−19 The image of a distant star produced by an astronomical telescope is a diffraction pattern. If the effective diameter of the objective lens is reduced by one-half by covering its outer parts with a stop, the area of the central maximum of the diffraction pattern is A. decreased by a factor of 4. B. halved. C. unchanged. D. doubled. E. increased by a factor of 4. 1986−I−22 In the diffraction of light round an obstacle, the angle of diffraction is increased when A. the wavelength of the incident light wave is increased. B. the wavelength of the incident light wave is decreased. C. the amplitude of the incident light wave is increased. D. the amplitude of the incident light wave is decreased. E. the width of the obstacle is increased. 1990−I−26 White light diffracted by a single slit falls on a white screen. Which of the following statements is/are correct ? (1) The centre of the diffraction pattern is white. (2) The first minimum is closer to the centre for red light than for blue light. (3) The central band width is increased as the slit width is increased. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only



<< Interference >> 1980−I−19

X and Y are two transparent but partially reflecting glass sheets, separated by a small distance l. when light of wavelength λ is incident normally on plate X, the light emerging from Y is of very low intensity when the distance l is equal to A. nλ / 2 B. (2n + 1)λ / 2 C. nλ D. (n + 1

4)λ E. (2n +1)λ / 4 1981−I−43 In a Young's slits experiment to produce interference fringes on a screen, the separation of the interference fringes is increased by increasing (1) the distance between the slits and the screen. (2) the wavelength of the light. (3) the distance between the source and the slits. A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct 1983−I−38 When monochromatic light is incident normally on a wedge-shaped thin film, an interference pattern may be seen by reflection. Which of the following changes would increase the number of fringes per unit length as seen by an observer ? (1) increasing the wavelength of the light (2) increasing the angle of the wedge (3) increasing the refractive index of the film material A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct 1984−I−15 Newton's rings produced when a biconvex lens rests on a plane glass plate are observed using a travelling microscope. If the biconvex lens is very slowly moved vertically upwards from the lower glass plate, which of the following would be observed ? A. Th e central spot remains dark all the time. B. The rings disappear immediately. C. The rings move towards the centre. D. The rings move out from the centre. E. The rings are no longer concentric. 1984−I−16



Young's slits are used to produce interference fringes with light of wavelength 600 nm. A thin sheet of mica of refractive index 1.6 is placed in front of one of the slits and the centre of the fringe-system is displaced through 8 fringe widths. The thickness of the mica is A. 120 nm B. 3000 nm C. 4000 nm D. 7700 nm E. 8000 nm 1985−I−18 The surface of a material of refractive index 1.8 is coated with a thin film of liquid of refractive index 1.5 and thickness 200 nm. White light falls normally on the thin film. Which of the following light wavelengths (in air) is not reflected from the thin film ? A. 400 nm B. 450 nm C. 600 nm D. 750 nm E. 800 nm 1988−I−23

When monochromatic light is incident normally on a wedge-shaped thin air film, an interference pattern may be seen by reflection. Which of the following is/are correct ? (1) Parallel fringes are observed. (2) If water is introduced into the region between the plates, the fringe separation decreases. (3) If the angle of the wedge is increased, the fringe separation decreases. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1987−I−24

A plane mirror M is illuminated by monochromatic light from a slit S. The virtual image of S by reflection and S itself act as 2 coherent sources and the interference pattern is observed on the screen AOB at a distance from the mirror. Which of the following statements about the interference pattern on the screen is/are correct ? (1) No interference pattern can be seen in the region OB on the screen. (2) As the mirror M moves downward, the separation of the fringes decreases. (3) As the mirror M moves horizontally away from the screen, the separation of the fringes increases.

A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only



1989−I−21 The coated lens of a camera appear purple in daylight. According to the manufacturers, the coating has a refractive index of 1.25 and the material of the lens has a refractive index of 1.50. If the wavelength of yellow light in air is 520 nm, the approximate thickness of the coating is A. 104 nm B. 130 nm C. 180 nm D. 210 nm E. 260 nm 1990−I−23

2 loudspeakers L1 and L2 are connected to a signal generator G. A microphone is moved along the line

AB and the variation in intensity is noted. Which of the following statements concerning the above arrangement is/are correct ? (1) If the separation of the 2 loudspeakers is less than the wavelength of the sound emitted, no

alternation of maxima and minima can be detected along AB. (2) If the frequency of the sound waves emitted is increased, the separation between adjacent maxima

along AB will be increased. (3) If the 2 loudspeakers are vibrating in antiphase, no alternation of maxima and minima will be detected

along AB. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1991−I−20 Orange light of wavelength 600 nm (in air) is incident normally from air onto a liquid film whose refractive index is 1.25. for what minimum value of film thickness will the greatest amount of light be transmitted through the film ? A. 120 nm B. 180 nm C. 240 nm D. 300 nm E. 480 nm 1991−I−22(For AL only) In an arrangement for viewing Newton's rings, if the lens which rests on a glass plate were moved slowly upwards by one wavelength (of the viewing light), which of the following would be observed ? A. The central spot becomes bright. B. The rings disappear. C. The rings move towards the centre. D. The rings move out from the centre. E. The rings are no longer concentric.



1992−I−22.

Two loudspeakers are connected to the same signal generator. A microphone positioned at X defects maximum intensity. When the microphone is moved upwards, maximum intensity is also detected at Y. Which of the following may give possible values of the wavelength of the sound emitted from the loudspeakers ? (1) 0.04 m (2) 0.08 m (3) 0.16 m A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1992−I−26

A ray AO of monochromatic light wavelength λ falls on a thin parallel-sided soap film of thickness t and refractive index n. Constructive interference will take place between rays M and N when A. nt = mλ B. nt = (m + 1/2) λ C. 2 nt = mλ D. 2 nt cos r = mλ E. 2 nt cos r = (m + 1.2) λ (m is an integer) 1995−IIA−15(AL) A coating material of refractive index 1.25 is used for the blooming of a lens having a larger refractive index. For normal incidence, if green light is to be transmitted in its greatest amount through the lens, which of the following thicknesses of the coating would do ? ( Given : wavelength of green light in air is 550 nm) (1) 137.5 nm (2) 220 nm (3) 330 nm A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)



1993−I−27

A loudspeaker L produces sound waves with frequency 1 000 Hz. the sound waves are reflected from a wall S. When a microphone M is moved between L and S, the loudness of the sound detected varies. (Speed of sound in air = 340 m/s) Which of the following statements is/are true ? (1) The variation in the loudness of the sound is due to diffraction. (2) The separation between consecutive positions of soft sound is 0.34 m . (3) Increasing the sound frequency will make the positions of soft sound closer. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) 1996−IIA−14(AL)

Monochromatic light of wavelength 589 nm is shone normally on a wedge-shaped thin air film to form interference fringes. If the distance between the sixth and ninety-sixth dark fringes is 15.8 mm, calculate the angle of wedge, θ. A. 0.024° B. 0.048° C. 0.072° D. 0.096° E. 0.190° 1997−IIA−15(AL)

In a young’s double slit experiment, light of wavelength 400 nm is used. If the path difference between the light from the two slits X and Y to a point P on the screen is 3000 nm, which of the following is/are correct? (1) P is the 7th dark fringe. (2) The fringe separation on the screen increases if the light source is moved closer to the slits. (3) P becomes a bright fringe if light of wavelength 500 nm is used A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)



1997−IIA−17(AL) In an arrangement for viewing Newton’s ring, which of the following would be observed if water is introduced to the space between the lens and the glass plate? A. The rings disappear. B. The central spot becomes bright. C. The separation between the rings increases. D. The rings shift towards the centre E. There is no observable change. 1999−IIA−12(AL)/9(AS) In a Young’s double slit experiment, a monochromatic light source of wavelength 700 nm is used and the separation of the slits is 0.1 mm. If 15 bright fringes are observed, what is the angle subtended by those fringes at the centre of the double slit ?

A. 4.8° B. 5.2° C. 5.6° D. 6.0° E. 6.4° 1999−IIA−13(AL)/10(AS) Two dippers S1 and S2 1.2 m apart are attached to a vibrator. They vibrate in phase in a ripple tank and generate waves of wavelength 0.8 cm.

Which of the following statements is/are correct? (1) S1 and S2 are positions of antinodes. (2) There is only one point between S1 and S2 which is always stationary. (3) The separation between two nearest antinodes between S1 and S2 is 0.4 cm A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)


Section B : Wave Motion (3. Electromagnetic Spectrum − M.C.) P.29

3. ELECTROMAGNETIC SPECTRUM (For AL only)

1980−I−16 Which of the following gives typical orders of magnitude of the wavelengths in metres of (1) infra−red rays (2) ultra−violet rays (3) medium−wave radio waves and (4) gamma radiation ? (1) (2) (3) (4) A. 102 10-4 10-2 10-7 B. 10-4 10-7 10-2 10-12 C. 10-7 10-4 102 10-12 D. 10-4 10-7 102 10-12 E. 10-2 10-4 102 10-7 1991−I−26 Ultrasonic waves are used instead of audible sound waves to measure the depth of the sea because (1) ultrasonic waves will not be interfered with by other sound waves in the water (2) ultrasonic waves can penetrate a greater depth of water with less spreading-out of waves. (3) small-sized objects can also be located. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1998−IIA−10 Which of the following travel(s) with the speed of light in vacuum?

(1) cathode rays (2) γ − rays (3) ultra violet radiation



Section B : Wave Motion (4. Stationary Wave − M.C.) P.30

4. STATIONARY WAVES 1992−I−23

Stationary wave patterns can be produced on an elastic string using the experimental set-up shown above by adjusting the frequency f of the vibrator. Which of the following statements concerning the experiment is/are correct ? (1) Stationary wave patterns can be observed for more than one value of the frequency f . (2) When the frequency f increases, the number of loops for the stationary wave pattern to be observed

also increases. (3) For a stationary wave pattern to occur, the length of the string must be equal to an integral number of

wavelengths. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1994−IIA−20

In the above experimental set-up, different stationary wave patterns are produced on an elastic string by adjusting the frequency f of the vibrator. Which of the following statements is/are correct ? (1) When f increases, the number of antinodes increases. (2) When f increases, the speed of the waves on the string increases. (3) The waves produced in air by the string has the same speed as the waves on the string. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)



4. STATIONARY WAVES

(For AL only) 1983−I−39 In a standing wave in a closed pipe, (1) some air molecules do not vibrate. (2) no energy comes out of the pipe. (3) in the fundamental mode of vibration air molecules in the middle of the pipe oscillate through a larger

amplitude than molecules at any other part of the pipe. A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct 1984−I−17 In the tuning of a violin string, a pitch pipe of frequency 427 Hz was blown at the same time as the string was plucked and 5 beats were heard every 2 seconds. Then the violin string was slightly tightened with a fine-adjustment screw. When the pitch pipe and the string were sounded together again no beats were heard. The initial frequency of the note produced by the string before any adjustment was made must have been A. 422.0 Hz B. 424.5 Hz C. 429.5 Hz

D. 432.0 Hz E. 437.0 Hz 1987−I−25 An open tube of length L and a string of length L produce the same fundamental note. However when each is sounded independently the sound produced can be distinguished readily. This is because

A. the string produces some harmonics which are not produced by the open pipe. B. the open pipe produces some harmonics which are not produced by the string. C. they produce completely different harmonics. D. the pipe produce longitudinal standing waves while the string produces transverse standing

waves. E. they produce the same harmonics but the amplitudes of corresponding harmonics are different.

1991−I−27

A stationary sound wave vibrating in its fundamental mode is set up in a tube closed at one end. P and Q are two points at the end and the middle of the tube aking its axis. Neglecting end-correction, what is the phase difference between the vibrations of the air molecules at points P and Q ? A. 0 B. 0.24π radian C. 0.5 π radian D. π radian E. 1.25π radian



1994−I−18

A stationary sound wave vibrating in its fundamental mode is set up in a pipe open at both ends. If an air particle at P oscillates with amplitude a, what are the amplitudes of oscillation of the air particles at Q and R ? (Neglect end corrections) Amplitude at Q Amplitude at R A. 0 a/2 B. a/2 0 C. 0 a D. a 0 E. a a 1997−IIA−16(AL) Two pipes A and B, with pipe A closed at one end and pipe B open at both ends, are sounded to give fundamental notes of the same frequency. The length ratio of pipe A to pipe B is A. 1 : 4 B. 1 : 2 C. 1 : 1 D. 2 : 1 E. 4 : 1 1998−IIA−16(AL)

The above figure shows a long vertical glass tube containing water. The water level is lowered until

the first resonance occurs when a vibrating tuning fork is placed at the opening of the tube. Which of the following statements is/are correct? (Neglect end correction)

(1) The sound produced by the air column above the water has the same frequency as the tuning

fork. (2) Resonance will occur again if the length of the air column above the water is increased to three

times its original value. (3) Resonance will occur if another tuning fork of twice the frequency is used. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)


Section B : Wave Motion (5. Acoustics − M.C.) P.33

5. ACOUSTICS (For AL only)

<< Intensity & loudness >> 1984−I−18 A sound reproduction system produces a sound level of 95 dB above threshold. Assuming the threshold of

hearing to be 10-12 Wm-2, 95 dB corresponds to an intensity of

A. 5.6 x 10-8 Wm-2 B. 0.00316 Wm-2 C. 0.0316 Wm-2

D. 1.12 Wm-2 E. 6.3 x 104 Wm-2 1986−I−27 If two independent sources, each separately at a noise level of 70 dB, are sounded together, they will produce a noise level of A. 35 dB B. 70 dB C. 73 dB D. 90 dB E. 140 dB 1987−I−27 If 3/4 of the sound energy produced by a typewriter is absorbed by a sponge rubber pad placed underneath, the sound level produced will fall by A. 0.25 dB B. 0.75 dB C. 3.00 dB D. 6.00 dB E. 12 dB 1988−I−26

The figure above shows the variation of the displacement of air molecules along the x-axis in a standing sound wave at a particular time. At what positions will the pressure remain constant with respect to time? A. x = 0 and x = 2a only B. x = a and x = 3a only C. x = 0 and x = a only D. x = 2a and x = 3a only E. x = 0 , x = a, x = 2a and x = 3a 1988−I−28 If the sound level of a source increases by 6 dB, the power emitted by the source will have its initial value multiplied by approximately

A. log10 6 B. 2 C. 4 D. 6 E. 106

1989−I−23

If the threshold of hearing is 10-12Wm-2, a sound level of one microwatt per m2 is above threshold by A. 6 dB B. 11 dB C. 60 dB D. 110 dB E. 120 dB



1990−I−18 Which of the following represent the approximate noise levels (i) in a quiet school library ? (ii) near the airport when an aircraft is taking off and flying overhead ? (i) (ii) A. 30 dB 60 dB B. 60 dB 90 dB C. 30 dB 90 dB D. 90 dB 60 dB E. 60 dB 30 dB 1992−I−21 A loudspeaker produces a sound intensity level of 80 dB at a point P. If the electrical power to the loudspeaker is halved, the intensity level at P will be

A. 20 dB B. 30 dB C. 40 dB D. 50 dB E. 77 dB 1993−I−25 A radio produces a sound intensity level of 50 dB at a point 2 m away from it. If the power output of the radio is doubled, what is the sound intensity level at a point 6 m from the radio ? ( You may regard the radio as a point source )

A. 30.9 dB B. 43.5 dB C. 46.5 dB D. 48.2 dB E. 49.7 dB 1995−IIA−19 Two loudspeakers are connected to the same signal source of negligible impedance. At a point equidistant from the two loudspeakers, a maximum intensity of intensity level 60 dB is detected. If one loudspeaker is disconnected, the intensity level at that point will be

A. 57 dB B. 54 dB C. 46 dB D. 30 dB E. 15 dB 1999−IIA−15 Students A and B are standing 5 m apart. A shout to B and the intensity level in db recorded by B is x. A then walks away from B so that they are 10 m apart. If A shouts again with the same power, what is the intensity level in db recorded by B? A. x/4 B. x/2 C. logx(x/4) D. x − 3 E. x − 6



<< Velocity of sound >> 1982−AL−41

The figure above shows each of the stationary traces S1 and S2 observed on the screen of a cathode ray

oscilloscope connected to a microphone, when two tuning forks F1 and F2 respectively are sounded in

turn. (The time base remains the same in each case.) Which of the following statements is/are correct ? (1) The period of F1 is greater than the period of F2.

(2) The pitch of F1 is greater than the pitch of F2.

(3) The speed of sound from F1 is greater than the speed of sound from F2.

A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct << Doppler effect >> 1980−AL−20 A man stands beside a railway track as a train approaches and then passes him, sounding its whistle all the time. The true frequency of the whistle is 99 Hz. The highest note the man hears is of frequency 110 Hz. What is the frequency of the lowest note which he hears ? A. 88 Hz B. 89 Hz C. 90 Hz D. 99 Hz E. 100 Hz



1983−I−16 An ambulance with its siren sounding a note of constant frequency fs drives along a straight road. Which of

the graphs below best represents the variation of frequency f heard by a man standing close to the road as the ambulance drives past ?

1985−I−42 A sound source S approaches an observer O at a constant speed v. Which of the following statements is/are correct ? (1) The frequency of the source as heard by O increases linearly with time as S approaches O. (2) The sound appears louder and louder as S approaches O. (3) The wavelength of the wave appears to be shorter as S approaches O. A. if (1), (2) and (3) are all correct B. if (1) and (2) only are correct C. if (2) and (3) only are correct D. if (1) only is correct E. if (3) only is correct



1986−I−26 An aeroplane flies horizontally at a low altitude with a constant speed of 300 m/s. It transmits a radio signal of frequency 30 MHz as it passes a receiving station. What is the difference in the frequencies received a long time before and a long time after the passage of the plane ? A. 10 Hz B. 30 Hz C. 60 Hz D. 120 Hz E. 150 Hz 1987−I−26 Two identical sound sources send out sound waves to an observer. One of the sources is now moved away from the observer. The observer then hears alternate loud and weak signals, and loud signals are detected whenever the source moves through a distance of 0.50 m. If the speed of the source is 1/10 of the speed of sound, the wavelength emitted by the stationary source is A. 0.25 m B. 0.45 m C. 0.5 m D. 0.55 m E. 1.00 m 1988−I−27 A moving train sounds a whistle of frequency 500 Hz. The apparent frequency heard by an observer standing close to the railroad is 462 Hz. If the speed of sound in air is 300 m/s, the train is moving at a speed of A. 23 m/s away from the observer. B. 23 m/s towards the observer. C. 25 m/s away from the observer. D. 25 m/s towards the observer. E. 28 m/s away from the observer. 1989−I−24 A stationary radar source emits waves of frequency f, and wavelength l which are reflected from an object moving towards the source at a speed u. The reflected waves reaching a receiver standing near to the radar source will have an apparent wavelength of A. l - 2u/f B. l - u/f C. l D. l + u/f E. l + 2u/f 1990−I−24 Sound waves of frequency f are emitted by a source S. When S is moved with speed u (relative to the ground) towards a stationary observer O, a rise in pitch of Df is detected. Which of the following statements is/are correct ? (1) The speed of sound waves relative to the observer is unaffected by the motion of S. (2) If both S and O move in the same direction with speed u, no rise in pitch will be detected. (3) If S is at rest with O moving towards it at speed u, the rise in pitch will also be Df. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only



1993−I−26 A hydrogen source in a laboratory emits a line spectrum with one of the lines having wavelength 656.3 nm. For a star receding from the earth at a speed of 200 km/s, what would be the wavelength of the corresponding line from the star observed on the earth ?(velocity of light = 3×108 ms-1 ) A. 655.5 nm B. 655.9 nm C. 656.7 nm D. 657.1 nm E. 657.5 nm 1994−IIA−19 An ambulance, sounding its siren to produce a note of 800 Hz, approaches a stationary pedestrian P at a steady speed of 40 m/s. Calculate the frequency of the sound heard by P. (Speed of sound in air = 340 m/s) A. 706 Hz B. 716 Hz C. 800 Hz D. 894 Hz E. 907 Hz 1995−IIA−18 An aircraft flies near the earth's surface over a stationary observed on a windless day. the frequency of the notes from the engine received by the observed is 300 Hz when approaching, and becomes 150 Hz when leaving. Assume the speed of sound in air to be 336 m s-1. The speed of the aircraft is

A. 56 m s-1 B. 84 m s-1 C. 112 m s-1 D. 168 m s-1 E. 224 m s-1 1996−IIA−20 3-cm microwaves are used in a radar speed trap. When the emitted and reflected signals are superposed, beats are produced. Find the minimum beat frequency above which a driver would be prosecuted for exceeding a speed limit of 100 km h-1 . A. 1000 Hz B. 1900 Hz C. 2400 Hz D. 3400 Hz E. 4700 Hz 1997−IIA−14 A moving ship sounds a foghorn and an echo is received from a cliff behind it. Which of the following wave characteristics of the original sound is/are difference from that of the echo? (1) frequency (2) amplitude (3) speed A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) 1999−IIA−14 On a straight road, a car and an ambulance move with uniform speeds u1 and u2 respectively (with u2 > u1) in the same direction. Initially the ambulance is behind the car and it overtakes the car after some time. The siren on the ambulance continuously emits a sound of a certain frequency. What is the ratio of the wavelength of sound received by an observer in the car before the ambulance overtakes to that after the ambulance overtakes?

A. 2

2

v u

v u

−+

B. 2

2

v u

v u

+−

C. 2 1

2 1

u u

u u

−+

D. 2 1

2 1

v u u

v u u

− ++ −

E. 2 1

2 1

v u u

v u u

+ −− +


Section B : Wave Motion (6. Optical instrument − M.C.) P.39

6. OPTICAL INSTRUMENTS

* For AS level, familiarity ONLY with magnifying glass, microscope, refracting telescope and camera from lower level is assumed. << Geometric Optics >> 1980−I−11/1980−I−7 A ray of light passes through a prism as shown. As the angle i is increased from zero to nearly 90o, the angle θ

A. decreases continuously B. increases continuously C. passes through a minimum value D. passes through a maximum value E. remains constant 1980−I−13 A beam of light is converging towards a point O 10 cm behind a convex mirror M, and on its axis. The beam is reflected by the mirror, and forms an images at a point I.

If the radius of curvature of M is 30 cm, what is the distance between the image I and the mirror M ? A. 6.0 cm B. 7.5 cm C. 12 cm D. 15 cm E. 30 cm 1980−I−14

What is the lowest possible refractive index for the material of a 90o prism used to reverse the direction of a ray of light by total internal reflection ? A. 1 / 2 B. 1 C. 2 D. 3 / 2 E. 2 2



1980−I−15 For which of the following object distances would a converging lens of focal length 30 cm form a real magnified image of the object ? A. 7.5 cm B. 15 cm C. 22.5 cm D. 40 cm E. 60 cm 1981−I−8

The diagram shows a converging lens L, of focal length of magnitude F, a convex mirror M of focal length of magnitude f, and the positions S at which an object is coincident with its own image. If SL = x and LM = u, then

A. 1 1 1x y F

+ = B. 1 1 1x y f F

++

= C. 1 1

21

x y f F+

+=

D. y + F = 2f E. xy F

f+ + =−( )1 1 1

1981−I−9 The image of an object formed on a screen by a thin converging lens has height a. By moving the lens towards the screen, a second lens positions is found at which the height of the image formed on the screen is b. What is the height of the height ?

A. 1

2( )a b+ B.

1

2ab C. ab

D. ab

3

E. ba

3

1982−I−14 When a diver looks up towards the surface from underwater, the surface behaves like A. a converging lens B. a diverging lens C. a plane mirror covering the entire surface D. a plane mirror with a circular hole in it. centred above the diver's head. E. a circular plane mirror of limited extent, centred above the diver's head. 1982−I−15 A near-sighted person's greatest distance of distinct vision is 0.9 m. His sight is improved by wearing spectacles which increase his greatest distance of distinct vision to 18 m. What is the magnitude of the focal length of the spectacle lenses ? A. 0.86 m B. 0.90 m C. 0.95 m D. 17.1 m E. 18.9 m



1983−I−13

A converging lens forms a sharp image on a screen as shown. A glass slab of thickness t is inserted between the lens and the screen. In order for the image to be again sharply focussed, it is necessary to move the screen a small distance d A. away from the lens; d decreases when t increases. B. away from the lens; d increases when t increases. C. towards the lens; d decreases when t increases. D. towards the lens; d increases when t increases. E. away from the lens; d is independent of t. 1983−I−14

When light is incident on the face AB of a prism as shown, it may pass through the face AC, with total deviation d, or it may suffer total internal reflection at AC. Which of the graphs below best represents the variation of d with i ? (t.i.r. represents total internal reflection) A. B.

C. D.

E.



1983−I−15

Two arrows are drawn as shown on a screen, placed at a distance 2 f from a converging lens of focal length f. Which of the following diagrams correctly represents the image seen when the screen is viewed through the lens ?

1984−I−13

The diagram shows two incoming parallel rays of light P and Q which pass through a thin converging lens L. The ray XY after passing through the lens will pass through the point A. I B. II C. III D. IV E. V



1985−I−15

The diagram above shows a small electric lamp fixed on a wall and positioned on the principal axis of a concave mirror of radius of curvature 12 cm. If the mirror is 24 cm from the wall, which of the following statements best describes the appearance of the reflected light on the wall ? A. It is in the form of a dot on the lamp. B. It is a circular patch on the lamp and the same size as the lamp. C. It is a circular patch round the lamp but smaller in size than the mirror. D. It is a circular patch round the lamp and the same size as the mirror. E. It is a circular patch round the lamp but larger in size than the mirror. 1985−I−21 A photograph is taken with a camera. The exposure time required with an aperture of f-4 is 1 s. The exposure time required with an aperture of f-8 is A. 0.25 s. B. 0.50 s. C. 1 s. D. 2 s. E. 4 s. 1985−I−39

A converging lens L and a lamp S are arranged as shown. The rays from S converge at a point I after passing through L. Which of the following operations could enable a parallel beam of light to emerge from the L ? (1) moving the lens L to the left until a parallel rays are obtained (2) replacing L by a lens with less converging power (3) placing a diverging lens of suitable focal length in front of the lens L A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only



1985−I−41 A train of plane wavefronts is incident upon a diverging lens. F denotes one of the focal points of the lens. Which of the following diagrams represent(s) what might happen to the wavefronts ? (1) (2) (3)

A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1986−I−18 When a parallel bean of white light passes through a glass lens, it is separated into rays of different colours. For which colour of light does the lens have the greatest focal length and for which colour of light does glass have the greatest refractive index ? The lens has the greatest Glass has the greatest focal length for refractive index for A. blue light blue light B. blue light red light C. yellow light yellow light D. red light blue light E. red light red light 1986−I−24 Lens Nature Focal length I converging 40 cm II converging 10 cm III diverging 40 cm IV diverging 10 cm A student is given the above 4 lenses, and asked to make a telescope which will give erect magnified final images. How should he choose the lenses ? objective eyepiece A. I II B. I III C. I IV D. II III E. II IV



1986−I−20 A real object is placed in front of a convex mirror of focal length f . Images are formed by the convex mirror for various object distances u. If the image distances are denoted by v, which of the graphs below shows the variation of v with u ?

A. B. C.

D. E.

1987−I−20

Rays from point light source O are reflected by a concave mirror M and converge to a point I as shown. Which of the following operations would enable a parallel beam of light to be reflected from M ? (1) moving the mirror M towards O (2) replacing M by a concave mirror of shorter focal length (3) placing a converging lens of suitable focal length between O and M A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only



1987−I−21

A real image I of an object is formed by a converging lens L as shown above. A diverging len L1 is placed between L and I such that a real image I’ is obtained. Which of the following statement is/are correct ? (1) I’ is an inverted image. (2) I’ is larger than I (3) I’ is further away from L than I. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1988−I−21

When a pin is moved along the principal axis of a small concave mirror, the image position coincides with the object at a point 0.5 m from the mirror. If the mirror is placed at a depth of 0.2 m in a transparent liquid, the same phenomenon occurs when the pin is placed 0.4 m from the mirror. The refractive index of the liquid is A. 6/5 B. 5/4 C. 4/3 D. 3/2 E. 5/3 1992−I−16 The image of an object formed on a screen by a convex lens has height a. By moving the lens towards the screen, it is found that there is a second lens position at which another image of height b is formed on the screen. The height of the object is A. (a + b)/2 B. a b2 2+ C. ab

D. a b3 / E. b a3 /



1992−I−17 The sun subtends an angle of 0.5° at the surface of the earth. A convex lens of focal length 100 cm is used to form an image of the sun onto a screen. The diameter of the image is about A. 1 mm B. 3 mm C. 5 mm D. 9 mm E. 50 mm 1995−II−17(AL)/1995−II−10(AS) When an object placed far away from a convex lens is gradually moved towards the lens, the separation between the object and its real image will A. decrease. B. decrease and then increase C. increase D. increase and the decrease E. remains unchanged 1994−II−21(AL)/1994−II−11(AS) Which of the following ray diagrams is/are correct ? (F is the focus of the corresponding optical instrument.)

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3) 1994−II−10AS) The speed of light in a certain material is 1.6 × 108 m s-1. Find the critical angle for that material and air. (Speed of light in air = 3 × 108 m s-1) A. 28.1o B. 32.2o C. 41.8o D. 48.0o E. 57.8o 1996−IIA−18(AL)

A small object O is placed at the focus of a convex lens L as shown. A concave mirror M is placed 80 cm behind the lens. If the focal length of L is 50 cm and the final image formed by this system is at infinity, the focal length of M is A. 20 cm B. 30 cm C. 40 cm D. 50 cm E. 60 cm



< Magnifying glass >> 1981−I−10

A converging lens of focal length 15 cm is used as a magnifying glass with the final image at infinity. If the least distance of distinct vision is 25 cm, the angular magnification achieved is

A. 0 B. 1 C. 53 D. 15 E. infinite

1986−I−19 A converging lens of focal length 12.5 cm issued as a magnifying glass with the final image formed at infinity. If the least distance of distinct vision is 25 cm, the angular magnification is A. 1/2 B. 1. C. 2. D. 4. E. infinite. 1993−I−23 An object placed in front of a magnifying glass forms an image at infinity with magnifying power 3. What is the focal length of the magnifying glass ? (you may assume the least distance of distinct vision to be 25 cm) A. 6.3 cm B. 8.3 cm C. 12.5 cm D. 25 cm E. 75 cm 1996−IIA−19(AL) The image of moon is focused on a screen by a converging lens of focal length 20 cm. If the moon subtends an angle of 9.5×10−3 radian at the center of the lens, calculate the diameter of the image. A. 4.8 ×10−2 cm B. 9.5 ×10−2 cm C. 1.9 ×10−1 cm D. 3.8 ×10−1 cm E 7.6 ×10−1 cm



<< Speed of light − measurement >> 1981−I−12 The diagram shows a mirror M which rotates about an axis through X with constant angular velocity w, and a spherical mirror Y whose centre of curvature is at X, where XY = r.

A narrow parallel beam of light strikes M at X, with angle of incidence q, such that it is reflected along XY and is again reflected by M, to form the emergent beam. What is the angle between the initial incident and final emergent beams ? (c is the speed of light.)

A. ωr

4c B.

ωr

2c C.

ωr

c D.

2ωr

c E.

4ωr

c

1982−I−16 A plane mirror is rotating with angular speed w. When pulses of light, of pulse frequency f, strike the mirror, they are reflected such that the angle between successive reflected pulses is q. If the direction of the incident pulses remains constant, the value of q is

A. wpf

B. w2pf

C. w4pf

D. wf E.

2wf

1992−I−19

Light is incident on an octagonal mirror and traverses a path ABCD, of total length L, before being reflected again from another face of the octagonal mirror. The octagonal mirror is rotated and its angular velocity adjusted until the light emerges in the same direction as when the mirror is stationary. If the speed of light is c, the smallest angular velocity to achieve this condition is A. πc/(8L) B. πc/(4L) C. πc/(2L) D. πc/L E. 2πc/L



<< Microscope >> 1981−I−46

The diagram represents a microscope with the object at A. The image of A in the objective is formed at B. Which of the following statements is correct ? (1) AO is less than fo

(2) BE is less than fe

(3) The image at B is real A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1985−I−40 In a compound microscope, (1) the final image produced is virtual. (2) the final image produced is erect. (3) the focal lengths of both the objective and the eyepiece must be long in order to produce high

magnification. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only



<< Telescope >> 1980−I−12 An astronomical telescope has an objective lens of focal length 42 cm and an eyepiece of focal length 7.0 cm. If the telescope is adjusted to form the final image at infinity, how far from the eyepiece would you place your eye to see the brightest image ? A. 6.00 cm B. 8.17 cm C. 8.40 cm D. 8.75 cm E. 20.0 cm 1982−I−13

L1 and L2 are converging lenses, each of focal length 50 cm. The final image of object O, formed by

refraction through both lenses, is at I. The distance OI is A. 54.5 cm B. 110 cm C. 200 cm D. 550 cm E. 605 cm 1984−I−12 An astronomical telescope has an objective of focal length 40 cm, and an eyepiece of focal length 2 cm. It is used to look at a distant object when its lenses are set 42 cm apart. The final image seen is A. upright, virtual and at infinity. B. inverted, virtual and at infinity. C. upright, real and at infinity. D. inverted, real and at infinity. E. upright, virtual and at the least distance of distinct vision. 1987−I−22

A distance object consisting of two arrows is viewed through an astronomical refracting telescope consisting if two converging lenses. Which of the following corresponds to the images seen ? A. B. C. D. E.

. . . . .



1990−I−20 In a simple astronomical telescope, under normal adjustment, which of the following statements is/are correct ? (1) The first image is formed at the focal length of the objective. (2) The first image is real and inverted. (3) The focal length of the objective is longer than that of the eyepiece. A. (1), (2) and (3) B. (1) and (2) only C. (2) and (3) only D. (1) only E. (3) only 1991−I−28 A simple two-convex lens refracting telescope has a magnifying power of 12.5 when the telescope is in normal adjustment. The focal length of the objective is 0.75 m. The separation between the objective and the eye piece is A. 0.06 m B. 0.69 m C. 0.81 m D. 1.35 m E. 16.7 m 1992−I−18 In an astronomical telescope set at normal adjustment, the focal lengths of the objective and the eyepiece are 50 cm and 10 cm respectively. Which of the following gives the separation of the lenses and the angular magnification of the telescope ? Lens separation Angular magnification A. 30 cm 5 B. 40 cm 0.5 C. 40 cm 5 D. 60 cm 0.5 E. 60 cm 5 1995−II−16(AL)/1995−II−9(AS) An astronomical refracting telescope consists of two converging lenes of focal lengths 100 cm and 5 cm. Under normal adjustment, it is used to observe a distant object which subtends an angle of 0.2o when viewed directly. Which of the following statements is/are correct ?

(1) The lens with focal length 5 cm should be the objective. (2) The height of the first image formed by the telescope is 3.5 mm. (3) The angle subtended by the final image seen by the observed is 4o. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)



1997−IIA−18(AL)

The above diagram shows two light rays from a point source O passing in turn through a convex lens L1 and a concave lens L2. Which of the following is true of the focal lengths of the lenses? Focal length of L1 Focal length of L2 A. 5 cm less than 10 cm B. 10 cm less than 10 cm C. 10 cm 10 cm D. 5 cm greater than 10 cm E. 10 cm greater than 10 cm 1999−IIA−10(AL)/8(AS)

A converging light beam is directed towards a convex mirror M. The reflected beam then passes through a convex lens L and forms an image at I. Which of the following about the focal lengths of M and L is correct? focal length of M focal length of L A. more than 4 cm 2 cm B. less than 4 cm 2 cm C. 4 cm 2 cm D. less than 4 cm 4 cm E. more than 4 cm 4 cm



1999−IIA−11(AL) An astronomical refracting telescope is adjusted to view a distant object under normal adjustment. Which of the following statement is/are correct? (1) The first image formed by the objective is real and is smaller than the object. (2) The final image formed by the eyepiece is at the least distance of distinct vision from the eye. (3) If part of the objective is blocked by an opaque obstacle, part of the final image could not be

viewed. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)


Section B : Wave Motion (1. Wave phenomenon - Interference − Structure-type-Question) P.55

1. WAVE PHENOMENA - INTERFERENCE 1982−IIB−6 A circular wire ring is dipped into soap solution and held vertically. When viewed in a dark room with monochromatic light of wavelength 6.5 × 10-7 m reflected normally from the film, a series of interference fringes are seen. The pattern of fringes at a particular instant is shown is Figure 1 (The refractive index of soap solution = 1.33)

Figure 1

(a) What colour are the fringes ? (b) Why is there dark area at the top of the ring ? (c) What is the thickness of the film at point A ? (d) As time goes on and if the film drains downwards and does not break, the fringe pattern changes

from that shown in Figure 1 describe the changes you would expect to see (explaination are not required).



1984−IIB−3 In Figure 2, the loudspeakers L1 and L2 placed 3 m apart are fed from a signal generator G, whose frequency is 600 Hz, so that they emit sound waves in phase. The speed of the sound waves is 340 m s-1.

Figure 2

(a) Describe the variation in the signal detected by a microphone when it moves slowly as follows :

(i) along line AB, the perpendicular bisector of L1L2 . (ii) along line XY, parallel to L1L2 and about 20 m away from it

(b) Point Z in Figure 2 represents a point at which a minimum intensity sound is heard. When the

loudspeaker L2 is temporarily disconnected, a student finds that the intensity of the sound heard at Z increases. He finds this difficult to understand, as disconnecting L2 presumably means that the total output energy from the loudspeakers decreases. Write a short note explaining the result to the student and explaining why it does not conflict with the law of conservation of energy.

(c) The loudspeaker L2 is now reconnected, but with the connections to its terminals interchanged, so

that it emits sound waves in antiphase with those from loudspeaker L1. Describe what effect, if any, this have on the signal received by a microphone placed along XY compared with the arrangement in (a)(ii).



1986−IIB−3

Figure 3 In the optical arrangement shown in Figure 3, monochromatic light from an extended monochromatic source S falls onto a thin, half-silvered mirror M. The incident light then divides into two beams, one proceeding by transmission towards mirror M1; the other proceeding by reflection towards M2. The beams are reflected at each of these mirrors and are sent back along their directions of incidence, each beam eventually entering the microscope. Due to the finite dimension of the source S, this produced divergent light rays which are incident at slightly different angles on M, and consequently and interference pattern of bright and dark fringes is observed on looking through the microscope. (a) Briefly explain how the bright and dark fringes are formed. (b) When a thin film is placed perpendicular to the light rays between M and M2, a shift of 7 fringes is

observed by the microscope. If the wavelength of the monochromatic light is 480 nm and the refractive index of the film is 1.45 at this wavelength, determine the thickness of the film.

(c) The thin film is then removed. The mirror M2is now moved at a constant rate in one direction, and

kept perpendicular to the light beam from M. 800 fringes are obsvered to cross the centre of the field of view. (i) Briefly explain this effect. (ii) How far has the mirror M2 been displaced ?

(d) The light source is now replaced by a sodium discharge tube which emits yellow light consisting of

two wavelengths, 589.0 nm and 589.6 nm. As M2 is again moved, it is observed that the interference pattern disappears and reappears periodically. Explain why this happens.



1987−IIB−3

Figure 4 A student tests the grinding of a lens surface by observing the appearance of Newton’s rings. The lens is placed in contact with a flat glass plate (as shown in Figure 4), and light from a sodium discharge lamp is shone on the lens from above. (a) If the rings are to be observed also from above, draw a labelled diagram of the experimental

arrangement he should use to view Newton’s rings. (b) How can he tell whether or not the ground lens surface is perfectly spherical ? (c) In observing Newton’s rings using reflected light, the central region is dark when the thickness of the air film at the centre is zero. Briefly account for this. (d) Draw a diagram showing the path of the rays which destructively interfere to form a dark ring. (e) If the student now replaces the lens by another plano-convex lens of shorter focal length, describe

and explain the changes in the fringe pattern observed. 1990−IIA−9

Figure 5

To measure the diameter of a metal wire, the wire is placed between two flat parallel-sided glass plates as shown in Figure 5, forming a wedge-shaped air film of length 80 mm. The plates are illuminated normally from above by sodium light of wavelength λ and interference fringes are observed from above. (a) Draw a labelled diagram of a suitable experimental arrangement which includes the apparatus of

Figure 5 to measure the separation between adjacent fringes. (b) Briefly explain the formation of the fringes and hence write down in terms of λ and t., the condition

for a bright fringe to be produced at a particular point where the separation of the plates is t (see Figure 5).

(c) In this experiment, the wavelength of the light is 600 nm, and the fringes are found to have a

separation of 0.16 mm. Calculate the diameter of the wire. (d) If the space in the wedge is filled with water of refractive index 1.33, what will happen to the fringe

pattern observed ? Explain your answer briefly.



1993−IIA−9 In Figure 6.1, a layer of material of refractive index 1.40 and thickness 3.0 × 10-5 m is coated uniformly on a glass block of refractive index 1.50. It is illuminated by light of wavelength 4.20 × 10-7 m from an extended source.

Figure 6.1 (a) What is the colour of the light ? (b) Calculate the wavelength of the light in the film. (c) For normal incidence,

(i) find the path difference between the lights reflected from the coating surface and from the coating-glass boundary;

(ii) explain what will happen when the two reflected waves recombine. (d) Figure 6.2 shows part of the interference pattern observed directly from above. Explain why such a

pattern is observed.

Figure 6.2 (e) Sketch the interference pattern if the coating is not on a glass surface but on the top of a transparent

block of refractive index 1.38. (f) Explain briefly the difference between the patterns in (d) and (e).



1999-IA-2 (a)

Diagram O represents the equilibrium positions of a line of equally spaced selected atoms in a metal.

When an ultrasonic wave of a certain frequency travels from left to right in the metal, the positions of the atoms at different times within a period are shown in diagrams P, Q and R.

(i) Which particles in diagram R correspond to rarefactions ? (ii) Find the wavelength, frequency and speed of the ultrasonic wave in the metal.

(b) A student uses the set-up in Figure 7 to find the speed of sound in air. The frequency of the signal generator is set at 2 kHz. When the microphone is moved vertically along PQ perpendicular to the bench, a series of alternating maximum and minimum signals are detected. The first maximum signal is found at P while Q corresponds to the fifth maximum. The separation between P and Q is found to be 1.1 m. (Note : The microphone detects the change in pressure caused by the sound waves.)

Figure 7

(i) When the microphone is moved on the bench between point P and the loudspeaker, maximum signals are detected. What can you say about the effect of reflection on a compression of the sound waves incident on the bench?

(ii) Draw on Figure 7 the two path along which sound waves propagate to Q from the

loudspeaker. Explain why a series of maximum and minimum signals are detected along PQ. (iii) Calculate the speed of sound in air. (Hint: Some of the sound waves can be treated as coming

from the mirror image of the loudspeaker below the bench.)


Section B : Wave Motion (2. Wave phenomenon - Diffraction grating − Structure-type-Question) P.61

2. WAVE PHENOMENA - DIFFRACTION GRATING 1980−IIB−3

Figure 7

In figure 7 a screen covered in graph paper measuring 0.6 m × 0.6 m is set up at a distance of 1 m from a diffraction grating measuring 0.1 × 0.1 m with 4 × 105 lines per metre. A line filament white light source in the focal plane of a convex lens is used to uniformly illuminate the grating surface. The lines of the grating are parallel to the source filament, and the whole set-up is arranged such that axis A passes through the centres of the screen, the grating, the lens, and the line filament (all of which are perpendicular to the axis A). (a) A filter passing only of wavelength 500 nm is placed between the source and the lens. In the space

below make a scale drawing of the pattern produced on the graph paper. Explain your reasoning. (b) A second lens is now placed between the grating and the screen touching the surface of the grating

so that the screen lies in the focal plane of this lens. Make a scale drawing of the new pattern below. Explain your reasoning. (c) The filter is now removed. Sketch the new pattern below, labelling significant features.



1981−IIB−3

Figure 8

Student A views a line filament lamp covered with a yellow filter through a diffraction grating with its lines parallel to the filament (Figure 8). The grating is held at one end of a metre rule which is aimed at the lamp. At the other end of the metre rule, a second rule is placed at right angles to the first rule. (a) Student A asks student B to move a pencil held vertically along the second rule and tells him to stop

when it coincides with the yellow band in the first image of the lamp as seen through the grating. If the distance between the first rule and the pencil is x = 0.37 m (see Figure 8) and the diffraction grating has 6.0 × 105 lines per metre, calculate the wavelength of the yellow light.

(b) If student B keeps moving the pencil along the second metre rule in the same direction, how many

more yellow bands will be encountered ? Explain. (c) If the filter is removed, sketch the full pattern seen by student A on both sides of the filament, in the

space below. Label significant features.



1988−IIB−9 Figure 9.1 shows a diffraction grating with a total of 10 000 parallel slits, each slit being 10-6 m from the next. Light of wavelength λ = 589.0 nm from a sodium vapour lamp falls perpendicularly onto the grating.

Figure 9.1 (a) (i) Calculate the angle θ in degree (to an accuracy of 3 decimal places) for the first order of

maximum intensity. (ii) What is the path difference BC (in terms of wavelength λ) between waves from the 1st and 10

000th slit ? (b) Now consider waves emerging at a slightly larger angle θ' such that the resultant amplitude of the

waves from all the slits in this new direction is zero. What is the path difference BC' (in terms of λ) between waves from the 1st and 10 000th slit ?

(Hint : consider the path difference between light from the slit pairs 1st and 5001st, 2nd and 5002nd etc.)

(c)

Figure 9.2

θ' is the angular position of the minimum intensity following the first order maximum intensity (Figure 9.2). Calculate the angular half-width [i.e. ( θ' − θ )] for the first order spectral line.

(d) Suppose the incident light contains another wavelength λ' = 589.6 nm. Can these two spectral lines

distinguished as two separate lines ? Explain your reasoning.



1994−IB−6(AL) (a) A student views a green light source through a multiple-slit setup which can be considered as a

diffraction grating with a few slits. The pattern observed as shown in Figure 10.1.

(i) How would the pattern be affected if red light is used instead ? (ii) Figure 10.2 shows the pattern observed by using another multiple-slit setup. Narrower bright

fringes are observed but their separation is the same as that in Figure 10.1. What can you say about the number of slits and the slit separation of this setup, compared with the first one ?

(b) (i) Figure 10.3 shows the essential features of a spectrometer. Necessary adjustments o the

collimator and the telescope have already been made. Draw on the figure two rays paths from the sodium lamp to the eye of an observed through the spectrometer.

Figure 10.3



(ii) To observed the spectrum of the sodium lamp, a student place a diffraction grating on the

platform of the spectrometer such that the incident light falls normally on the grating. The sodium lamp produces yellow light of two slightly different wavelengths. The student uses the second-order images and records the angular position readings of the two yellow lines on such side of the central image as follows :

Left-hand side (second order)

Right-hand side (second order)

first line second line first line second line angular position reading 45°36 ' 45°40 ' 134°22 ' 134°26 '

Given the grating constant (i.e. the slit separation) to be 1 684 nm, calculate the two wavelengths of the yellow light produced by the sodium lamp. (iii) Suggest ONE reason for making measurements by using the second-order images instead of

the first-order ones.


Section B : Wave Motion (3. Wave phenomenon - Polarisation − Structure-type-Question) P.66

3. WAVE PHENOMENA - POLARIZATION 1995−IA−3(AL)

Figure 19

Figure 19 shows a section of a continuous plane polarized electromagnetic wave of frequency 10 000 MHz travelling in space at a certain time. The vectors in x-direction represent the varying electric field travelling along positive z-direction. (a) What is represented by the vectors in y-direction ? (b) Using the reference frame provided below, sketch the wave form at a time 0.5 × 10-10 s later.

(c) An antenna ion the form of a straight rod is used to receive the electromagnetic wave. How should the antenna be orientated so that maximum signal (induced e.m.f. in the rod) is obtained ? Explain briefly.

(d) What happens to the signal received by the antenna in (c) when a grid of parallel conducting wires is placed in front of the antenna, with the conducting wires (i) parallel to x-direction, (ii) parallel to y-direction. Explain briefly.

(e) If an antenna is in the form of a plane circular loop, how should it be orientated to receive maximum signal ? Explain briefly.


Section B : Wave Motion (4. Stationary Wave − Structure-type-Question) P.67

4. STATIONARY WAVE 1994−I−8(AS) Figure 12.1 shows the appearance of a stationary wave set up in an elastic string stretched between a vibrator and a stand. The vibrator is driven by a signal generator.

Figure 12.1

(a) Briefly explain the formation of the stationary waves. Explain also why the mid-point of the string C,

is stationary all the time. (b) The pattern shown in Figure 12.1 occurs when the signal generator output frequency is 40 Hz.

(i) Find the period of oscillation of point B on the string. (ii) If a stroboscopic lamp is employed for 'freezing' the pattern, suggest THREE frequencies of

the lamp under which point B would be 'frozen' at a single position.


Section B : Wave Motion (4. Stationary Wave − Structure-type-Question) P.68

1995−IB−7(AL) A student uses the apparatus shown in Figure 13 to determine the speed of sound in air. A loudspeaker L, is connected to the signal generator and a microphone, M, is connected to the Y-input and the earth terminal of a CRO. The loudspeaker L and the reflecting plate R are placed on a meter rule (not shown) with the microphone M between plate.

Figure 13

(a) Give one property that the reflecting plate should have. (b) With the signal generator set at a frequency, briefly describe the procedures you would follow to set

up stationary sound waves between the loudspeaker and the reflecting plate. (c) With the stationary wave set, the microphone M is moved along the axis of the loudspeaker and the

trace on the CRO screen is seen to vary in size. Consecutive positions of M are recorded whenever the trace has its smallest amplitude. The procedure is repeated for different signal frequencies. The results are recorded in Table 13 below :

Frequency of

signal generator/kHz

Positions of M corresponding to the smallest amplitude of the CRO trace/cm

Wavelength λ/cm

Period T/ms

2.500 2.941 3.571 4.545 6.250

27.0, 34.0, 41.0, 47.9, 54.5, 61.6, 68.7 16.0, 22.0, 28.1, 33.7, 39.6, 45.7, 51.5 18.7, 23.7, 28.4, 33.3, 38.4, 43.5, 48.1 31.8, 35.8, 39.8, 43.6, 47.4, 51.5, 55.5 26.4, 29.4, 32.4, 35.2, 38.2, 41.5, 44.7

Table 13 (i) Show clearly how you determine the wavelength of sound in air by using the data

corresponding to the frequency 2.500 kHz. (ii) Complete Table 13 and plot a graph of wavelength λ against period T. (iii) Hence find the speed of sound in air. (iv) Why did the student not use frequencies of uniform intervals, say for example, of 0.5 kHz ? (v) Explain why the graph does not pass through the origin.

(d) Explain an advantage of performing the experiment outdoors. Suggest one remedial measure when

doing the experiment indoors.


Section B : Wave Motion (5. Acoustics − Structure-type-Question) P.69

5. ACOUSTICS 1980−IIB−4

Figure 11 In Figure 11, AB represents the threshold of heating for the average human ear, and GH represents the discomfort loudness level. (a) CD and EF represent curves of equal loudness. What are their loudness ? (b) Considering a frequency range of 300 Hz to 3000 Hz, determine the average intensity level of a

source emitting these frequencies which would produce discomfort giving your answer in dB. (c) What is the dB level difference between the required intensities of 1 000 Hz and 16 000 Hz sources

which would give the same loudness level corresponding to curve CD ? (d) If the distance of the 1 000 Hz source in (c) from the hearing ear is d, estimate the distance it will

have to be moved so that it cannot be heard.



1985−IIB−5 (a) (i) A certain machine in a factory produces a 65 dB sound level when operated. Taking Io as the

threshold of hearing, calculate the maximum number of machine which can be operated at the same time in the factory if the noise level is not permitted to exceed 72 dB.

(ii) Suppose the ventilation system of the factory produces a background noise level of 4.5 dB. Would the total noise level exceed the noise limit 72 dB when the maximum number of machines [as found in (i)] are operating in the factory ? Explain your answer.

(b) The following table shows some typical situations in everyday life. State the approximate noise-levels

found in these situations.

Situation Noise level / dB (i) Quiet places such as libraries and hospital wards (ii) Normal traffic noise in Hong Kong (iii) Noise at a level which humans cannot bear

(c) Name one design feature used to lower the noise levels in buildings built near airports or busy

highways. 1996−IA−3 (a) A police car and a lorry are moving with the same speed, u, towards each other. The siren on the

police car emits sound waves of frequency 1000 Hz and the velocity of sound in air is 300 m s−1. (i) With the aid of a diagram, derive the expressions for the wavelength, λ’, and the frequency,

f’, of the sound waves heard by the driver of the lorry. (4 marks) (ii) When the police car passes the lorry, the frequency of the sound waves heard by the driver of

the lorry suddenly drops by 200Hz. Calculate the speed of the police car. (4 marks) (b) State and explain one piece of evidence which suggests that the universe is expanding.

(4 marks)



1997−IA−2 A small source emitting electromagnetic waves of frequency 1010 Hz is placed some distance, say 100 m, from a 1 m × 1 m square metal plate. The line joining the source and the centre of the plate is perpendicular to the plate. Figure 2.1 shows part of the wavefronts emitted from the source towards the plate.

Figure 2.1

(a) Name the electromagnetic waves emitted (1 mark) (b) (i) In Figure 2.1, sketch the reflected wavefronts and indicate the position S’ where the reflected

wavefronts appear to come from. (2 marks) (ii) A detector registers a non-zero reading when it is placed some distance behind the plate on

the line joining the source and the centre of the plate. Briefly explain this observation with the aid of a diagram (2 marks)

(c) (i) If the plate is now moving towards the source at a speed of 20 m/s, what would the speed of

position S’ in (b) (i) be Hence or otherwise calculate the change in frequency of the reflected waves. (3 marks)

(ii) A typical radar speed trap employs similar principles by sending some electromagnetic waves towards a moving car. To deduce the speed of the car, the reflected waves received are compared with the emitted waves in such a way that the beat frequency between them can be measured. Explain why the beat frequency is measured instead of the frequency of the reflected waves being directly measured. (2 marks)



1997−IA−3 Figure 3.1 shows a uniform wire which is held taut but unstretched between a fixed point and a smooth cylindrical peg of radius 1 cm. The force constant of the wire is 9.6 × 102 N/s. the tension in the wire can be increased by rotating the peg about its fixed axis so that some wire is wound onto the peg.

Figure 3.1 (a) When the peg is rotated through an angle of 2π , calculate (i) the tension in the wire (2 marks) (ii) the work done in rotating the peg (2 marks) (b) The above wire is part of a musical instrument. Two knife edges, A and B, are placed 0.36 m apart

under the stretched wire as shown in Figure 3.2. The mass of the wire between A and B is 6.4 × 10−

4 kg (Assume that the presence of the two knife edges would not affect the tension in the wire)

Figure 3.2 (i) Calculate the frequency of the fundamental note emitted when the wire between A and B is

plucked. (3 marks) (ii) State THREE differences between the waves in the wire and the fundamental note emitted.

(3 marks) (iii) Draw a diagram to show the vibration of the wire between A and B when it is vibrating at the

third harmonic. (1 mark)



1999−IA−6(AL) (a) For a source emitting electromagnetic waves of frequency f and moving towards an observer with a

velocity v, the frequency of the electromagnetic waves received by the observer is given by

12

12

v1

cf ' fv

1c

+ = −

If v << c, show that equation (*) can be approximated to v

f ' f 1c

= +

.

(b) An earth satellite in an orbit near the earth’s surface emits a radio signal of frequency 100 MHz. When the satellite passes over a tracking station on the earth’s surface, the station detects beats between the received signal and the station’s own signal of frequency fo. The beat frequency keeps on decreasing from an initial value of 7000 Hz to 2000 Hz within minutes. (The satellite can be considered as moving horizontally with constant velocity during the period of observation).

(i) Explain why the beat frequency changes gradually and not abruptly. (ii) Find the speed of the satellite observed from the tracking station. (iii) Calculate the frequency fo of the station’s own signal. (Give your answer up to 6 sig.fig.) (iv) A student thinks that the calculated value in (ii) is the orbital speed of the satellite. Do you

agree with him? Explain briefly.


Section B : Wave Motion (6. Optical instrument − Structure-type-Question) P.74

6. OPTICAL INSTRUMENT AND GEOMETIC OPTICS 1980−IIB−2

Figure 14

Figure 14 shows the variation of the angular deviation of a light ray incident upon a triangular glass prism with angle of incidence i. (a) Determine the vertex angle of the prism. (b) Calculate the refractive index of the prism material (c) If the light originally was blue, and this was replaced by red light, discuss qualitatively the effects of

this change on the position of the point P on the new graph of d against i ? Give your reasoning. 1982−IIB−5 .

Figure 15

A ray of light is incident centrally at the end face of a cylindrical-shaped optical light-guiding fibre, at an angle of incident of 38o with the central axis. The refractive index n of this optical fibre varies with the radial distance r from the axis as

n = 1.45 - 0.09 r, where r is expressed in mm. (a) Calculate the angle of refraction θ of the light ray at the first end face. (b) At a certain point within the optical fibre, the light ray turns back towards the central axis. Find the

distance of this point from the axis. (c) Explain why it is more suitable to use an optical fibre to convey a ray of light than to use a hllow tube

of small cross-section with a reflective inner surface.



1989−IIA−9

Figure 16

A student set up two converging lenses to form a simple type of astronomical telescope for use in normal adjustment. Light rays X, Y and Z from a distant object fall upon the objective lens as shown in Figure 16. The focal lengths of the objective and the eyepiece are 50 cm and 10 cm respectively. (a) Draw the paths for X, Y and Z as they pass through the telescope, showing how they emerge from

the eyepiece. (b) Use your diagram to explain the meaning of angular magnification of the telescope. How is this

related to the focal lengths of the lenses ? (c) (i) What is meant by the eye-ring of a telescope ?

(ii) Outline the steps you would take to determine experimentally the position of the eye-ring of this telescope.



1991−IIA−9

Figure 17.1 Figure 17.1 shows the main parts of an apparatus used to determine the speed of light c. (a) When the rotating mirror is stationary, an image of the illuminated slit at P is produced back at P.

State the condition required. Explain your answer briefly. (b) When the mirror is rotating at n rev s-1, the image of P becomes displaced to Q. The reflected ray

suffers an angular displacement of θ. (i) Why is the image displaced ? (ii) Derive a mathematical relationship between the angular displacement of the image θ and the

speed of light c. (c)

Figure 17.2

In practice, the angular displacement θof the image is very small and difficult to measure accurately.

An improved version of the apparatus replaced the rotating mirror with a rotating octagon with reflecting surfaces as shown Figure 17.2. the speed of the rotating octagon is adjusted till there is no displacement of the image on the screen. (i) Explain how this is possible. (ii) If the lowest speed of rotation for the image to remain in the same position is 3000 rev s-1 and

the separation between the rotating octagon and the fixed mirror is 6 km, calculate the speed of light c.



1994−IA−2(AL) (a)

Figure 18.1 A student uses two converging lenses to set up a compound microscope in normal adjustment.

Figure 18.1 shows two light rays, P and Q, from the top of an object falling on the objective lens of the microscope. The foci of the objective lens are denoted by FO and the foci of the eyepiece are denoted by FE. (i) On Figure 18.1, complete the ray paths for P and Q as they pass through the microscope,

showing how the final image is formed. (ii) Indicate on Figure 18.1 the visual angle β subtended by the final image at the eye of an

observed using the microscope. (iii) Distinguish between linear magnification and angular magnification. (iv) Find the angular magnification of the microscope in terms of the height of the object, ho, and

the height of the final image, hi. Show your working. (Take the least distance of distinct vision to be D)

(b) Figure 18.2 shows four light ray from an object passing through a microscope in normal adjustment.

R and S come from the top of the object, T and U from the bottom. R and T pass through the top of the objective lens, S and U pas through the bottom.

Figure 18.2

(i) On Figure 18.2, X is the best position for the eye to view the image. With reference to the ray diagram, briefly explain the advantage(s) of choosing X as the viewing position.

(ii) Why should the diameter of the beam at X be no wider than about 2 mm ?



1998−IA−3(AL) A monochromatic light ray enters a glass sphere of radius 5.0 cm from air as shown in Figure 3.1. The incident ray is parallel to the diameter AOB with a separation of 4.5 cm. After entering the glass sphere, the ray crosses the diameter AOB at a certain point between centre O and point B.

Figure 3.1 (a) Mark on Figure 3.1 the angle of incident i and angle of refraction. (2 marks) (b) Calculate the angle of incidence i. (1 mark) (c) If the angle of refraction is 28.6°, calculate the refractive index of the glass sphere. (2 marks) (d) If the frequency of the light ray is 5.4×1014 Hz, find its wavelength insider the glass sphere.

(3 marks) (e) If the glass sphere is immersed in water (refractive index = 1.33), would the light ray intersect the

diameter AOB before it leaves the sphere ? Explain briefly. (3 marks)


Section B : Wave Motion (1. Wave propagation, Wave phenomenon − Essay-type-Question) P.79

1. Wave propagation, Wave Phenomena [Wave phenomena - Interference, polarisation, diffraction] 1980−IIA−4 (For ASL, partially restricted only) Compare the physical processes of propagation for (i) light waves and (ii) sound waves. Continue your comparison of these waves by considering the phenomena of (a) polarization, (b) interference and (c) diffraction, giving a practical example of each of these for each type of wave. Briefly indicate how you would determine experimentally the wavelengths of light and sound waves. [Wave phenomena - Interference] 1982−IIA−3 Explain from first principles the following phenomena : (a) The colours observed when viewing an oil film on water, giving the reasons why film must be thin,

and (b) the absence of high frequencies to an observer standing outside and to the side of an open door

leading into a room where music is being played. (Consider velocity of sound=340ms-1.) [Wave phenomena - Interference, refraction, Wave-particle duality] 1983−IIA−4(a) (a) By considering one practical example of each of the following phenomena :

(i) the refraction of light, and (ii) the interference of light show how these phenomena can be explained by assuming that light possesses a wavelike

nature. ( Note : No mathematical derivations are needed for (ii).)

[Wave Propagation] 1984−IIA−4 The concept of waves can be applied to (1) a musical sound, and (2) a V.H.F. radio transmission. For these two types of waves describe (a) their main propagation characteristics, (b) their normal frequency ranges, and (c) methods for measuring the intensity of the wave (one method for each type of wave). Simple block

diagrams and only brief explanations of the method are required.

[Wave-particle duality] 1989−IIA−3(part (b) & (c) are restricted to AL only) (a) Describe the main characteristics of light when considered as

(i) a wave propagation , and (ii) moving particles.

(b) Give a brief account of an experiment which illustrates the wave nature of light AND a second experiment which illustrates its particle nature (no mathematical derivations expected).

(c) Explain how it is possible to reconcile the wave/particles natures of electrons.



[Wave phenomena - Interference] 1985−IIA−2 (a) State the principle of superposition for waves. Use this to explain the production of sound beats, and

derive an expression for their frequency. (b) Use the principle of superposition to account for the observed phenomenon of interference, and state

clearly the necessary physical conditions. Discuss the particular difficulties encountered in satisfying these conditions for normal light waves (not laser light), and state how these are overcome.

(c) A rectangular wire frame is completely immersed in a soap solution and withdrawn carefully so that a soap film is stretched across the whole frame. Due to gravitational force and evaporation, the cross-section of the film will vary roughly with time as follows:

(1) (2) (3) 1 minutes 2 minutes 3 minutes

Give a qualitative account of what you would expect to observe during these 3 minutes if the film

were illuminated by monochromatic light from behind the observer. Give brief explanations. (d) Suggest any one practical use for light interference (only brief details are required.) [Wave phenomena - refraction, diffraction grating] 1986−IIB−3 (part (b) & (c) are restricted to AL only) (a) Explain, by using wave-front diagrams, how the wave theory of light is able to explain

(i) the refraction, and (ii) the dispersion of a narrow light beam incident upon the interface of two different optically transparent media.

(b) Draw a diagram showing the ray paths through a prism spectrometer when a lines spectrometer

when a line spectrum is observed, and explain the necessary optical adjustments of the collimator and telescope.

(c) Suggest possible advantages of replacing the prism by diffraction grating. [Wave phenomena - refraction, diffraction] 1987−IIA−3 Both light and sound can be considered as wave propagation of energy. (a) Carefully compare the main characteristics of such waves and their propagation. (b) Distinguish between

(i) refraction and (ii) diffraction for a sound wave, giving one practical example of each.

(c) Briefly explain why diffraction is more difficult to observed in 'everyday life’ for light rather sound.



[Wave phenomena - interference] 1988−IIA−3 (a) A long slinky spring is laid flat on a horizontal table and slightly stretched. Briefly explain how you

would produce two transverse pulses moving along the spring in opposite directions from each end, when the amplitudes are (i) in the same direction and (ii) in opposite directions. Draw suitable diagrams showing the progression of the pulses along the spring, through its centre.

(b) By reference to the results of (a) explain the main effects of the principle of superposition on interfacing waves.

(c) Describe, qualitatively, the phenomenon of wave interference and give one example, each, for (i) sound and (ii) light, which may be experienced in daily life. (No mathematical derivation are required.)

(d) Explain clearly the necessary conditions for observable interference to take place between (i) sound waves and (ii) light waves, briefly contrasting any main difficulties encountered in satisfying such conditions.

[Wave phenomena - Interference, diffraction, diffraction grating] 1991−IIA−3 (a) By considering the propagation of light waves through slit(s), carefully distinguish between diffraction

and interference. (b) Explain why interference of light is not observed when

(i) two separate light sources are used and (ii) the path difference between light rays from the same light source is too great.

(c) Draw a diagram showing what you would expect to observe when viewing through a diffraction grating the vertical glowing filament of an electric lamp, place several meters away. The grating is placed with its ruled lines parallel to the filament. Briefly explain the observations you make.

[Wave propagation] 1992−IIA−3 (a) Demonstrate the difference between

(i) transverse wave propagation, (ii) longitudinal wave propagation, by drawing graphical plots showing the corresponding variations of the displacements of the medium particles with distance from the source for times t = 0, T/4, T/2,and 3T/4, where T is the wave period.

(b) Describe an experiment to show the phase change of the particle oscillations with distance from a sound wave source, and hence explain how you would determine wave propagation speed.

(c) How does the propagation of light waves differ from that of sound waves ?



[Wave propagation, Beats, Doppler’s Effect] 1993−IIA−2(part (b) and (c) are restricted to AL only) (a) Describe FOUR contrasting features of progressive and stationary waves, and state the conditions

necessary for a stationary wave. (b) Beats can be heard when a tuning fork and a guitar string vibrate simultaneously with slight different

frequencies f1 and f2 respectively. (i) With the aid of diagrams, explain how beats are formed. Draw a diagram to show the resulting

wave form. (ii) Show that the beat frequency is equal to the difference between f1 and f2 .

(c) Briefly describe how the principle of beats would be used to detect the speed of cars in a police radar speed check system. (No mathematical derivation is expected.)

[Wave propagation - Huygens’ Principle] [Wave phenomena - Interference] 1994−IIB−2(AL) (a) State Huygens’ principle. With the aid of diagrams, use the principle to explain

(i) how the direction of propagation of a plane wave is related to the wavefront; (ii) why plane waves refract as they pass from one medium to another.

(b) (i) Explain why interference patterns cannot be successfully produced with two small, close light sources.

(ii) Explain, with the aid of a diagram, how the problem in (i) is overcome in Young’s experiment. (iii) Describe and account for the observed interference pattern.

(c) Describe and explain one practical use for light interference. [Wave phenomena - Interference, diffraction grating] 1994−IA−2(AS) (a) Explain from first principles the periodic fading of television reception due to low-flying aircraft. (b) Give a reason why two light bulbs on a ceiling do not produce and observable interference pattern.

Explain briefly. (c) (i) In a double-slit experiment using light of wavelength λ and slits with separation d, show that

the angular position, θ, of bright fringes measured from the normal to the double slits, satisfy the relation d sin θ = nλ where n is an integer.

(ii) With the aid of a diagram, describe the explain how to measure the wavelength of light by considering the positions of two bright fringes in a double-slit experiment.

(d) State the similarities and differences between the interference patterns produced by a diffraction grating and by double slit having the same slit separation. The light source used as a filament lamp.

[Wave phenomena - polarisation]



1995−IIB−3(a)-(b) (AL) (For AL only) (a) Unpolarised sunlight is incident horizontally on air molecules around O in the earth's atmosphere. Part

of the light is transmitted horizontally and part is scattered vertically downward.

Briefly explain which ray, the transmitted one or the scattered one, is plane polarised and give the

direction of the electric field vector for this ray. Describe a method to identify this polarised light ray. (b) Give an amount of an everyday example involving polarised light. [Acoustics] [Wave phenomena - Interference] [Geometric optics] 1995−IIB−3(AS) (a) (i) Discuss the ways in which sound waves differ from electromagnetic waves.

(ii) Describe and explain the use of sonar and radar as navigational aids for ships, that is helping them to avoid running ashore or colliding with other ships.

(b) Suppose the speeds of light in air and in glass are v1 and v2 respectively. With the aid of a wavefront diagram, derive an equation relating the refractive index of glass n and the speeds of light in the two media.

(c) With the aid of a diagram, explain qualitatively why different colours are observed on a soap bubble under sunlight.

[Wave phenomena - diffraction grating] 1995−IIB−5(a)(AL) (a) Describe an experiment for measuring the wavelength of monochromatic light using a spectrometer

and a diffraction grating with a known grating spacing.

[Wave propagation]



[Wave phenomena - interference] [Acoustics] 1996-IIB-2(AL) (a) (i) For a sound wave of constant amplitude and frequency travelling through air, sketch a graph to

show the time variation of the displacement of the vibrating air particles at a point in the path of the wave. Using the same time axis, sketch also the variation of air pressure with time at the same point.

(ii) What is the phase relationship between the displacement and the air pressure in (a)(i)? (b)

Two identical loudspeakers connected to the same signal generator are placed inside a room as

shown. All the surfaces of the room are covered with sound-absorbing material. Point O is equidistant from the loudspeakers and line XOY is parallel to the line joining the loudspeakers. The variation of sound intensity along XOY is shown below:

(i) Explain why (I) the graph shows alternative maximum and minimum (II) the sound intensity at a minimum point is non-zero. (ii) State clearly the difference between sound intensity and sound intensity level. Explain why the

sound intensity level at 0 would decrease by 6 dB if one loudspeaker is turned off. (iii) Explain the change(s), if any, in the variation of sound intensity along XOY if the frequency of

the signal generator is increased.

(c) With the aid of a diagram, describe an experiment to find the speed of sound in air by using Kundt’s tube together with a loudspeaker. State any precautions which should be taken in the experiment and explain what would be observed.



[Wave propagation] [Wave phenomena - interference, diffraction] 1996-IIB-2(AS) (a) (i)

The diagram shows the positions of the particles, which are equally spaced when undisturbed,

in a wave at times 0 s, 0.01 s and 0.02 s. State TWO properties of the wave and find its wavelength and frequency.

(ii) Explain how a note is produced when blowing across the top of a test tube. If the tube is filled with some water, state how the frequency of the note would be affected. (No mathematical derivation is required.)

(b)

Two loudspeakers connected to the same signal generator are placed inside a room as shown

on the previous page. All the surfaces of the room are covered with sound-absorbing materials. Point O is equidistant from the loudspeakers and line XOY is parallel to the line joining the loudspeakers. A microphone, which is connected to a CRO, is moved along XOY to detect the sound. The variation of the amplitude of the CRO trace with the position of the microphone is shown below:

(i) Explain why

(I) the graph shows alternative maximum and minimum (II) amplitude of the CRO trace at a minimum point is non-zero.

(ii) Explain the change(s), if any, in the variation of the amplitude of the CRO trace with the position of the microphone if the frequency of the signal generator is increased.

(iii) Music covering a wide range of frequencies is being played through one of the loudspeakers, and the door of the room is open. A student walks out of the room and stands to one side of the door. Explain the differences between the sound heard by the student before he walks out of the room and when he is outside it.



[Wave phenomena - interference, diffraction grating] 1997-IIB-2(AL) (a) Plane monochromatic light waves of wavelength λ are incident normally onto a plane transmission

grating of slit separation d to produce an interference pattern. (i) Using the principle of superposition describe briefly how the principal maxima are formed and

deduce the formula for the angular positions of the principal maxima. (ii) It is preferable to measure the wavelength of light by using a plane transmission grating rather

than using a double slit. Explain briefly. (b) Describe an experiment for observing the absorption spectrum of iodine using a diffraction grating.

Describe the spectrum observed and account for it in terms of the quantum nature of light and atomic structure.

(c) Briefly explain the principles involved in identifying the elements present in the atmosphere of the sun through studying the sun’s spectrum

[Wave phenomena - interference, diffraction grating] (a) With the aid of labelled diagrams, describe an experiment to show the diffraction and refraction of 3

cm microwaves. (b) Plane monochromatic light waves of wavelength λ are incident normally onto a plane transmission

grating of slit separation d to produce an interference pattern. (i) Using the principle of superposition describe briefly how the principal maxima are formed and

deduce the formula for the angular positions of the principal maxima. (ii) It is preferable to measure the wavelength of light by using a plane transmission grating rather

than using a double slit. Explain briefly. (c) (i) Explain why an oil film on water shows different colours under sunlight. (ii) Describe how the flatness of a glass plate can be tested. (No mathematical derivation is required) [Wave phenomena] 1999−IIB−2(a)(AL)/(AS) (a) (ii) Explain the following referring to various phenomena of waves:

(I) Radio waves of long wavelengths can propagate long distance. (II) The voice of one of your teachers can be heard and identified before he enters the

classroom. (III) Two violin players are playing the same note together for a few seconds and a listener

finds that the intensity of the sound seems to vary with time. (IV) A radio receive seems to work better in some parts of a room than in other parts. (V) Polaroid sunglasses can effectively reduce the glare of the sun reflected from the sea.

(b) You are asked to measure the wavelength of red light using a diffraction grating. With the aid of a diagram, describe how you would carry out the experiment and state any precautions. List the measurements that you would take and the major source of error.


Section B : Wave Motion (2.Stationary Wave − Essay-type-Question) P.87

2. Stationary Wave, Resonance

1990−IIA−3(part (c) is restricted to AL only) (a) Explain the formation of stationary waves along a stretched wire which vibrates with a frequency f

and is fixed at both ends, giving graphical representations of the motion amplitude at difference positions along the wire corresponding to time intervals of 1 /(4f). What are the appropriate conditions for such stationary waves to occur ?

(b) Suggest a possible experimental method for demonstrating such stationary waves and determining the necessary conditions.

(c) Using this as an example explain the meaning of resonance. Briefly explain how such a phenomenon could occur and be observed in (i) an a.c. electrical circuit, and (ii) atoms. [No theoretical derivations required.]

1993−IIA−2(a) (a) Describe FOUR contrasting features of progressive and stationary waves, and state the conditions

necessary for a stationary wave. 1999−IIB−2(a)(i) With the aid of a diagram, explain how stationary waves are formed.


Section B : Wave Motion (3. Acoustics − Essay-type-Question) P.88

3. Acoustics (AL only)

[Wave propagation, Beats, Doppler’s Effect] 1993−IIA−2(b)- (c) (AL only) (b) Beats can be heard when a tuning fork and a guitar string vibrate simultaneously with slight different

frequencies f1 and f2 respectively. (i) With the aid of diagrams, explain how beats are formed. Draw a diagram to show the resulting

wave form. (ii) Show that the beat frequency is equal to the difference between f1 and f2 .

(c) Briefly describe how the principle of beats would be used to detect the speed of cars in a police radar speed check system. (No mathematical derivation is expected.)

[Doppler’s Effect] 1995−IIB−3(a)(AS) (a) (i) Discuss the ways in which sound waves differ from electromagnetic waves.

(ii) Describe and explain the use of sonar and radar as navigational aids for ships, that is helping them to avoid running ashore or colliding with other ships.

[Sound intensity, Speed of sound] 1996-IIB-2(b)(AL) (b)

Two identical loudspeakers connected to the same signal generator are placed inside a room as

shown. All the surfaces of the room are covered with sound-absorbing material. Point O is equidistant from the loudspeakers and line XOY is parallel to the line joining the loudspeakers. The variation of sound intensity along XOY is shown below:

(i) Explain why (I) the graph shows alternative maximum and minimum (II) the sound intensity at a minimum point is non-zero. (ii) State clearly the difference between sound intensity and sound intensity level. Explain why the

sound intensity level at 0 would decrease by 6 dB if one loudspeaker is turned off. (iii) Explain the change(s), if any, in the variation of sound intensity along XOY if the frequency of

the signal generator is increased.

(c) With the aid of a diagram, describe an experiment to find the speed of sound in air by using Kundt’s tube together with a loudspeaker. State any precautions which should be taken in the experiment and explain what would be observed.


Section B : Wave Motion (4. Optical instrument − Essay-type-Question) P.89

4. Optical instrument [Telescope, microscope] 1980−IIA−2 (For AL only) Compare the uses of two spaced converging lenses to form (a) a microscope and (b) a telescope, by drawing ray diagrams showing the formation of the final viewed images for each instrument when adjusted for normal use. In each case determine the angular magnification and explain how by design this may be kept high. What are the advantages of using mirrors rather than lenses in telescopes ? [Prism spectrometer] 1981−IIA−2 (For AL only) (a) Give a comprehensive account of a prism spectrometer, illustrating your answer with a ray diagram

showing the formation of the viewed spectrum of while light and explain in the necessary optical adjustments of the instrument before use (excluding the leveling of the table).

(b) Briefly explain the change in the spectrum of the light emitted by an iron bar as it is gradually heated up in a flame.

[Magnifying glass] 1988−IIA−2 (a) The human eye functions as a converging lens of variable focal length. Explain why the apparent sizes

of the Moon and a dollar held at arm's length seem similar. (b) When a single converging lens is used as magnifying glass the viewed imaged may be formed at

(i) infinity or (ii) the distance of nearest clear vision from the eye. Using a ray diagram show which of these arrangements gives the greatest magnification. What

is the physical factor limiting the magnification ? (c) Show, using a ray diagram, the it is possible to further increase the magnification by using an

additional converging lens. (No mathematical treatment involving the lens equation is required.)

[Geometric optics] 1995−IIB−3(b)(AS) (b) Suppose the speeds of light in air and in glass are v1 and v2 respectively. With the aid of a wavefront

diagram, derive an equation relating the refractive index of glass n and the speeds of light in the two media.


Section B : Wave Motion (4. Optical instrument − Essay-type-Question) P.90

[Telescope] 1998−IIB−2 (a) Explain what is meant by the normal adjustment for an astronomical refracting telescope and why it

is used in this way. (b) (i) Draw a diagram to show the passage of three light rays passing through an astronomical

refracting telescope from a point on a distant object (not on the axis of the telescope) when it is used with normal adjustment. Mark the foci of the objective lens (Fo) and eyepiece (Fe) clearly on your diagram. State the functions of the objective lens and eyepiece.

(ii) What is the meaning of the magnifying power of the astronomical refracting telescope with

normal adjustment? State the ways of increasing the magnifying power and discuss the limitations on its value.

(iii) What is the major disadvantage of the astronomical refracting telescope for viewing objects on the ground? With the help of a suitable diagram, show how this disadvantage can be overcome.

(c) An astronomical refracting telescope may not be able to produce bright images due to reflection from

the lens surfaces. Describe and explain a way to reduce the amount of reflected light from the lens surfaces. Why does the objective lens of such a telescope look purple in colour? (No mathematical derivation is required.)

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