AS Physics

WavesProgressive waves (travelling

waves) transfer energy from one place to another.

There are two types of waves ….

Transverse waves have oscillations perpendicular to the direction of travel of the wave

Longitudinal waves have oscillations parallel to the direction of travel of the wave

Frequency is the number of waves or oscillations per second

Wavelength is the distance between the same point on two successive waves

Sound WavesSound waves are

longitudinal waves consisting of compressions and rarefactions. Sound waves are in fact pressure waves.

Longitudinal Waves Applethttp://www.cbu.edu/~jvarrian/applets/

waves1/lontra_g.htm

http://www.ngsir.netfirms.com/englishhtm/Lwave.htm

http://www.mta.ca/faculty/science/physics/suren/Lwave/Lwave01.html

Electromagnetic WavesThere are seven

electromagnetic waves….

Radio, micro, IR, light, UV, x-rays and gamma rays

All of these can travel through a vacuum and travel at the speed of light

These waves are transverse and are made of vibrating electric and magnetic fields.

Transverse Waves Applethttp://surendranath.tripod.com/Applets/

Waves/Twave01/Twave01Applet.html

http://www.ngsir.netfirms.com/englishhtm/TwaveA.htm

http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm

The Wave EquationSpeed = frequency x wavelength

c = f x λ

Frequency = 1/ time periodf = 1/T

Speed or velocity (m/s)Frequency in Hertz (Hz)Wavelength (m)Time period in seconds (s)

Answers to past paper questionsQuestion 2a. Longitudinal: sound, ultrasound or seismic p-wavesTransverse: any electromagnetic wave, seismic s-

wavesbi.Frequency is the number of

waves/vibrations/oscillations per second/unit timebiiPeriod is the time taken for 1 complete cycle / wave /

vibration / oscillationciAmplitude = 4 x 10-5 m

Answers to past paper questionsQuestion 2ciiParticle at A moves 4 x 10-5m in one direction

parallel to the direction of the wave and then returns to its original equilibrium position before moving 4 x 10-5m in the opposite direction

(three marks for.... idea that the particle is vibrating or moves in one

direction and then the opposite direction....the movement of the particle is in the same

direction as the direction of the wave because the wave is longitudinal in nature.....

inclusion of magnitude of the distance moved)

Answers to past paper questionsQuestion 2ciiiSimilarity – same amplitude/frequency/period or

both move longitudinallyDifference – particles at A and B are out of phase

or have a phase difference of 180 degrees or π radians.

ivWavelength – 0.8mvFrequency = c/λ = 340/0.8 = 425 Hz(three marks from stating the equation, showing

working and the final answer)

Answers to past paper questionsQuestion 4

ai amplitude = 3.8 cmaii displacement = -3.4 cm (one mark for negative

sign)aiii period = 2.66 msaiv frequency = 1 / T = 1 / 2.66 x 10-3 = 376 Hz(student lose one mark if they have not taken into

account the idea that the time period was in milliseconds!)

b wavelength = c/f = 3 x 108 / 376 = 0.798 m(one mark for working out and one mark for final

answer)

Polarisation ExperimentDescribe the apparatus used.

What is true about the microwaves leaving the microwave transmitter?

What is true about the microwave receiver?

What did you observe to happen to the strength of the microwaves received, as the receiver was rotated through 360 °?

Was the effect any different when the transmitter was rotated?

What affect did the metal grille have on the strength of the microwaves detected?

Polarisation SummaryWaves are polarised if

the vibrations stay in one plane.

Waves are unpolarised if they vibrate in many planes.

Only transverse waves can be polarised.

RefractionRefractive index = Speed of light in a vacuum

Speed of light in a substance n = c / cs

Dense materials, that slow down light significantly, have larger refractive indexes. Refractive index does not have a unit.

The refractive index of air or a vacuum is 1.

RefractionLight undergoes total internal reflection when moving from a dense to

a less material at an angle of incidence greater than the critical angle.Sin θc = n2 / n1

Note material 1 is always denser and material 2 less dense hence n2 is always smaller.

Optical Fibres

Optical fibres transmit light by total internal reflection.Some have a core and a cladding. The cladding has a lower

refractive index than the core. In the absence of cladding, light could pass from one

optical fibre into another, if the two were in optical contact and the fibre surface was scratched or contain moisture.

Multipath dispersion causes the light signal to become ‘smeared’.

Optical Fibres Past Paper Question 3

ai cladding has a lower refractive indexaiiAngle of incidence must be greater than the

critical angle at the boundary between the core and the cladding

bMultipath dispersion occurs when different rays of

light travel different distances because they take different routes through the fibre. The different rays hence arrives at the end of the fibre at different times and this produces a spread out signal which is lower in quality.

Optical Fibres Past Paper Question 3

ciMaterial 1 is the core and material 2 is the cladding....sin θc = n2 / n1

0.98 = sin θc hence θc = 78.50

ciiIf the critical angle is large only a small proportion of

the light rays are captured by the optical fibre and undergo total internal reflection. These are the light rays that are almost horizontal and hence hitting the boundary at a very large angle of incidence. These light rays are travelling very similar distances down the fibre because they are taking very similar paths through the fibre and this reduces multipath dispersion.

Standing WavesA standing or stationary wave is

formed when two waves of the same frequency travelling in opposite directions at the same speed, with the same amplitude, undergo superposition.

Standing waves contain nodes and antinodes.

Nodes are points of zero amplitude and antinodes are points of maximum amplitude.

The distance between two nodes is half a wavelength.

On either side of a node the vibration is π radians out of phase and between two nodes all particles vibrate in phase.

SuperpositionThe principle of superposition states

that....‘when two waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point’.

When two waves arrive at a point exactly in phase, with a phase difference of 0 or 2π radians, constructive interference or reinforcement occurs to produce a maximum (called an antinode in the case of a stationary wave)

When two waves arrive at a point exactly out of phase, with a phase difference of π radians, destructive interference or cancellation occurs to produce a minimum (or node in the case of a stationary wave.)

Interference of LightLasers produce monochromatic coherent

light waves. Coherent waves have the same frequency and a constant phase difference. When coherent waves undergo superposition they produce a stable interference pattern.

Young’s Double Slit Experiment Coherent laser light diffracts (spreads out)

as it passes through each of the double slits. The diffracted light beams overlap. An interference pattern is produced on the screen with bright and dark fringes of equal width.

Young’s Double Slit ExperimentA bright fringe is produced when two

coherent light waves arrive at the screen..........

exactly in phasewith a phase difference of 0 or 2π radiansconstructive interference or reinforcement

occurs to produce a maxima

A dark fringe is produced when two coherent light waves arrive at the screen..........

exactly out of phasewith a phase difference of π radiansdestructive interference or cancelation

occurs to produce a minima

Young’s Double Slit Experiment and Path Difference

A bright fringe is produced when two coherent light waves arrive at the screen exactly in phase, with a phase difference of 0 or 2π radians and a path difference of a whole number of wavelengths (nλ). Constructive interference or reinforcement occurs to produce a maxima.

A dark fringe is produced when two coherent light waves arrive at the screen exactly out of phase, with a phase difference of π radians and a path difference equal to (n + ½) λ. Destructive interference or cancelation occurs to produce a minima.

Young’s Double Slit Experiment Fringe spacing (w) is the

distance from the start of one bright fringe to the start of the next bright fringe.

w = λD / s

λ is wavelength (m)D is the distance from the

screen to the double slit (m)s is the slit separation (m)

Diffraction by a single slitWhen light passes through a

single slit, the light also produces a pattern of bright and dark fringes.

This interference pattern is different to that observed in Young’s double slit experiment in two ways.....

the central bright fringe is twice the width of all other bright fringes (in Young’s experiment all fringes are the same width)

The intensity of the light is less for those bright fringes further from the central maximum (in Young’s experiment all bright fringes have the same intensity)

Diffraction GratingsA diffraction grating contains many

parallel slits (instead of the two used in Young’s slit experiment)

The grating produces bright maxima at discrete points on the screen again due to the principle of superposition.

The diffraction grating equation is....nλ = d sin θλ is the wavelength of the light (m)d is the grating spacing or the distance

from one slit to the next e.g. if a diffraction grating has 300 lines (or slits) per mm

d = 0.001 m / 300 = 3.3 x 10-6 mn is the order number (1, 2, 3 etc) of

the maximaangle θ is the angle to each maxima

Using the Diffraction Grating EquationPage 207 question 1 Laser light of wavelength 630 nm hits a

diffractiongrating of 300 lines per mm. Calculate the angle of diffraction of

each ofthe first two orders.....d = 1 mm / 300 = 0.001 m / 300 = 3.3 x 10-6 mnλ = d sin θ therefore sin θ = nλ/dFor the first order.......sin θ = 1 x 630 x 10-9 / 3.3 x 10-6 = 0.191 θ = 11.00

For the second order.......sin θ = 2 x 630 x 10-9 / 3.3 x 10-6 = 0.382 θ = 22.40

The number of diffracted orders produced....For n = 3, sin θ = 3 x 630 x 10-9/3.3 x 10-6 = 0.573, θ = 34.90

For n = 5, sin θ = 5 x 630 x 10-9/3.3 x 10-6 = 0.955, θ = 72.60

For n = 6, sin θ = 6 x 630 x 10-9/3.3 x 10-6 = 1.15Therefore five diffracted orders are produced.

Deriving the Diffraction Grating EquationIf these two light rays are to

produce a maxima on the screen, one light ray needs to have travelled a distance = nλ further than the other.

The light ray travelling though the top slit will have travelled distance AC further than the other light ray.

Angle ABC = θsin θ = AC / dwhere d is slit separationAC = d sin θ = n λd sin θ = n λ

Diffraction gratings split or disperse white light into a spectrum in a similar way to a glass prism. Light from stars produce absorption spectra containing dark lines. These dark absorption lines tell astronomers which elements are present in the star and the approximate surface temp of the star.