Download - Unit 4 REVISION PowerPoint
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WavesWaves can transfer energy and information without a net motion of the medium through which they travel.
They involve vibrations (oscillations) of some sort.
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Wave frontsWave fronts highlight the part of a wave that is moving together (in phase).= wavefrontRipples formed by a stone falling in water
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Rays Rays highlight the direction of energy transfer.
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Transverse wavesThe oscillations are perpendicular to the direction of energy transfer.Direction of energy transferoscillation
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Transverse wavespeaktrough
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Transverse wavesWater ripples
Light
On a rope/slinky
Earthquake S
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Longitudinal wavesThe oscillations are parallel to the direction of energy transfer.
Direction of energy transferoscillation
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Longitudinal wavescompressionrarefraction
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Longitudinal wavesSound
Slinky
Earthquake P
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Displacement - xThis measures the change that has taken place as a result of a wave passing a particular point. Zero displacement refers to the average position.= displacement
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Amplitude - AThe maximum displacement from the mean position.amplitude
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Period - TThe time taken (in seconds) for one complete oscillation. It is also the time taken for a complete wave to pass a given point.One complete wave
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Frequency - fThe number of oscillations in one second. Measured in Hertz.
50 Hz = 50 vibrations/waves/oscillations in one second.
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Wavelength - The shortest distance between points that are in phase (points moving together or in step). wavelength
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Wave speed - vThe speed at which the wave fronts pass a stationary observer.330 m.s-1
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Period and frequencyPeriod and frequency are reciprocals of each other
f = 1/TT = 1/f
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The Wave EquationThe time taken for one complete oscillation is the period T. In this time, the wave will have moved one wavelength .
The speed of the wave therefore is distance/time
v = /T = fLets try some questions
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A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving?A water wave travels through a pond with a speed of 1m/s and a frequency of 5Hz. What is the wavelength of the waves?The speed of sound is 330m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound?Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light?Some example wave equation questions0.2m0.5m0.6m/s3x108m/s
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Representing wavesThere are two ways we can represent a wave in a graph;
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Displacement/time graphThis looks at the movement of one point of the wave over a period of time1
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Displacement/time graphThis looks at the movement of one point of the wave over a period of time1PERIODIMPORTANT NOTE: This wave could be either transverse or longitudnal
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Displacement/distance graphThis is a snapshot of the wave at a particular moment1Distance cm-1-20.40.81.21.6displacement cm
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Displacement/distance graphThis is a snapshot of the wave at a particular moment1Distance cm-1-20.40.81.21.6displacement cmWAVELENGTHIMPORTANT NOTE: This wave could also be either transverse or longitudnal
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Wave intensityThis is defined as the amount of energy per unit time flowing through unit area
It is normally measured in W.m-2
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Wave intensityFor example, imagine a window with an area of 1m2. If one joule of light energy flows through that window every second we say the light intensity is 1 W.m-2.
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Intensity at a distance from a light sourceI = P/4d2
where d is the distance from the light source (in m) and P is the power of the light source(in W)
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Intensity at a distance from a light sourceI = P/4d2
d
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Intensity and amplitudeThe intensity of a wave is proportional to the square of its amplitude
I a2
(or I = ka2)
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Intensity and amplitudeThis means if you double the amplitude of a wave, its intensity quadruples!
I = ka2
If amplitude = 2a, new intensity = k(2a)2 new intensity = 4ka2
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Electromagnetic spectrum 700 - 420 nm 10-7 - 10-8 m 10-9 - 10-11 m 10-12 - 10-14 m 10-4 - 10-6 m 10-2 - 10-3 m 10-1 - 103 m
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What do they all have in common? 700 - 420 nm 10-7 - 10-8 m 10-9 - 10-11 m 10-12 - 10-14 m 10-4 - 10-6 m 10-2 - 10-3 m 10-1 - 103 m
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What do they all have in common?They can travel in a vacuumThey travel at 3 x 108m.s-1 in a vacuum (the speed of light)They are transverseThey are electromagnetic waves (electric and magnetic fields at right angles to each oscillating perpendicularly to the direction of energy transfer)
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RefractionWhen a wave changes speed (normally when entering another medium) it may refract (change direction)
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Water wavesWater waves travel slower in shallow water
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Sound wavesSound travels faster in warmer air
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Light wavesLight slows down as it goes from air to glass/water
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Snells lawThere is a relationship between the speed of the wave in the two media and the angles of incidence and refractionirRay, NOT wavefronts
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Snells lawspeed in substance 1 sin1speed in substance 2 sin2
=
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Snells lawIn the case of light only, we usually define a quantity called the index of refraction for a given medium asn = c = sin1/sin2cmwhere c is the speed of light in a vacuum and cm is the speed of light in the medium
vacuumccm
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Snells lawThus for two different media
sin1/sin2 = c1/c2 = n2/n1
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Refraction a few notesThe wavelength changes, the speed changes, but the frequency stays the same
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Refraction a few notesWhen the wave enters at 90, no change of direction takes place.
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DiffractionWaves spread as they pass an obstacle or through an opening
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DiffractionDiffraction is most when the opening or obstacle is similar in size to the wavelength of the wave
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Diffraction patterns HL later!
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DiffractionDiffraction is most when the opening or obstacle is similar in size to the wavelength of the wave
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DiffractionThats why we can hear people around a wall but not see them!
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Diffraction of radio waves
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Superposition
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Principle of superpositionWhen two or more waves meet, the resultant displacement is the sum of the individual displacements
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Constructive and destructive interferenceWhen two waves of the same frequency superimpose, we can get constructive interference or destructive interference.
+=+=
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SuperpositionIn general, the displacements of two (or more) waves can be added to produce a resultant wave. (Note, displacements can be negative)
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Interference patternsRipple Tank Simulation
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If we pass a wave through a pair of slits, an interference pattern is produced
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Path differenceWhether there is constructive or destructive interference observed at a particular point depends on the path difference of the two waves
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Constructive interference if path difference is a whole number of wavelengths
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Constructive interference if path difference is a whole number of wavelengthsantinode
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Destructive interference if path difference is a half number of wavelengths
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Destructive interference if path difference is a half number of wavelengthsnode
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Phase differenceis the time difference or phase angle by which one wave/oscillation leads or lags another. 180 or radians
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Phase differenceis the time difference or phase angle by which one wave/oscillation leads or lags another. 90 or /2 radians
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Simple harmonic motion (SHM)periodic motion in which the restoring force is proportional and in the opposite direction to the displacement
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Simple harmonic motion (SHM)periodic motion in which the restoring force is in the opposite durection and proportional to the displacement
F = -kx
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Graph of motionA graph of the motion will have this form
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Graph of motionA graph of the motion will have this formAmplitude x0Period T
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Graph of motionNotice the similarity with a sine curveangle
2 radians/23/22
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Graph of motionNotice the similarity with a sine curveangle
2 radians/23/22Amplitude x0x = x0sin
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Graph of motionAmplitude x0Period T
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Graph of motionAmplitude x0Period Tx = x0sint
where = 2/T = 2f = (angular frequency in rad.s-1)
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When x = 0 at t = 0Amplitude x0Period Tx = x0sint
where = 2/T = 2f = (angular frequency in rad.s-1)
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When x = x0 at t = 0Time displacement
Amplitude x0Period Tx = x0cost
where = 2/T = 2f = (angular frequency in rad.s-1)
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When x = 0 at t = 0Amplitude x0Period Tx = x0sint v = v0cost
where = 2/T = 2f = (angular frequency in rad.s-1)
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When x = x0 at t = 0Time displacement
Amplitude x0Period Tx = x0costv = -v0sint
where = 2/T = 2f = (angular frequency in rad.s-1)
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To summarise!When x = 0 at t = 0 x = x0sint and v = v0cost
When x = x0 at t = 0 x = x0cost and v = -v0sint
It can also be shown that v = (x02 x2) and a = -2x
where = 2/T = 2f = (angular frequency in rad.s-1)
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Maximum velocity?When x = 0
At this point the acceleration is zero (no resultant force at the equilibrium position).
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Maximum acceleration?When x = +/ x0
Here the velocity is zero
amax = -2x0
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Oscillating springWe know that F = -kx and that for SHM, a = -2x (so F = -m2x)
So -kx = -m2xk = m2 = (k/m)Remembering that = 2/TT = 2(m/k)
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S.H.M.Where is the kinetic energy maxiumum?
Where is the potential energy maximum?
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It can be shown that.Ek = m2(xo2 x2)ET = m2xo2Ep = m2x2
where = 2f = 2/T
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DampingIn most real oscillating systems energy is lost through friction.
The amplitude of oscillations gradually decreases until they reach zero. This is called damping
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UnderdampedThe system makes several oscillations before coming to rest
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Overdamped The system takes a long time to reach equilibrium
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Critical dampingEquilibrium is reached in the quickest time
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Natural frequencyAll objects have a natural frequency that they prefer to vibrate at.
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Forced vibrationsIf a force is applied at a different frequency to the natural frequency we get forced vibrations
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ResonanceIf the frequency of the external force is equal to the natural frequency we get resonanceYouTube - Ground Resonance - Side ViewYouTube - breaking a wine glass using resonancehttp://www.youtube.com/watch?v=6ai2QFxStxo&feature=relmfu
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