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1.   Considering a transverse wave, explain the following terms
a) crest and trough
  b) amplitude
  c) frequency
d) wavelength
  e) velocity of propagation
2.   Explain the following terms (using diagrams where necessary):
  a) interference
  b) diffraction
  c) refraction
3.   Calculate the frequency of
  a) red light of wavelength 650nm
  b) violet light of wavelength 420nm
4.   What is the wavelength of x rays of frequency 1018Hz
5.   What is the wavelength of sound of frequency 440Hz.
    The speed of sound in air is about 340ms-1.
6.   A transverse wave of frequency 5Hz moves along a spring at a speed of 1ms-1.
    At t=0 seconds, point p on the spring is at its maximum displacement of +2cm.
    Points A, B and C are points further along the spring (in the direction of motion of the wave).
  distance p-A=0.40m
  distance p-B=0.50m
  distance p-C=0.55m
    Find the displacements of points A, B and C at
  a) t=0
  b) t=0.20s
  c) t=0.25s
  d) t=0.30s
7.   A tube, closed at one end, is found to have a fundamental frequency of resonance, fo=200Hz.
    The length of the tube is 40cm
  a) Calculate the speed of sound in the tube
  b) What is the wavelength of the sound at resonance (frequency, fo).
  c) What are the frequencies of the next two harmonics of the same tube?
8.   The diagram below shows a stationary wave on a wire under tension.
    The frequency of the oscillations is 1200Hz.
  a) If the length of the wire is 40cm, calculate the speed of the waves moving along it.
  b) What will happen to the speed of waves moving along the wire if
    i)  the tension is doubled (all other factors remaining the same)?
    ii) the length is doubled (all other factors remaining the same)?
9. A tuning fork is held near the open end of a pipe which is closed at the other end.
    The fork is vibrating at 440Hz.
    The length of the air column in the pipe is varied.
    The first resonance is heard when the length of the pipe is 18.75cm.
  a) What is the next length at which resonance will be heard, with the same tuning fork?
  b) Calculate the speed of sound in the pipe.
10.   Two pipes are closed at one end and open at the other end.
    One pipe has a length of 30.0cm and the other has a length of 30.5cm.
    The pipes have the same diameter and therefore the same end-correction of 0.5cm.
  a) Calculate the beat frequency which would be heard if both the pipes are caused to resonate at
    i)  their fundamental frequency (first harmonic)
    ii) their first overtone (second harmonic).
    Assume the speed of sound is 330ms-1
b) Explain why beats would not be heard if two pipes having lengths of 30cm and 60cm were sounded together.
11.   A transverse sinusoidal wave is represented by the following equation
    Assuming that the units of the quantities in the equation are metres and seconds, find
  a) the amplitude of the wave
b) the wavelength
  c) the time period
  d) the velocity of propagation (state the direction of propagation)
  e) the average transverse speed of a particle in the medium through which the wave is moving.
12.   Two waves are represented by the following equations
  a) Calculate the velocities of the two waves.
  b) If these two waves move along the same string, what will be the distance between two adjacent nodes of the standing wave which they produce?
13.   A stationary wave is represented by the following equation
  a) What is the amplitude of oscillation at an anti-node?
  b) What is the wavelength of the travelling waves which produced this stationary wave?
  c) What type of wave is this? (light wave, sound wave, water wave etc; explain your choice)
14.   Young’s experiment is performed using a white light source with a red filter placed in front of it.
    The experiment is performed in a completely dark room so that very low levels of light can be observed.
  a) Describe and explain the pattern which is observed on the screen.
  b) How will the pattern change if the red filter is removed and a blue filter is put in its place?
  c) What will be seen on the screen if one of the slits is covered with:
    i)  a piece of metal
    ii) a thin sheet of transparent plastic of refractive index n=1.5
  d) What will be seen on the screen if the red and blue filters are put in front of the light source at the same time?
15.   A diffraction grating produces an image at an angle of 12.47° to the normal.
    The wavelength of the light being used is 600nm.
    The next order image is at an angle of 16.74° to the normal.
  a) the order of the image at 12.47°
  b) the number of lines per millimetre on the grating
  c) the maximum order of image which could be observed (using this grating and light of wavelength 600nm).
16.   A car is being driven towards a cliff at 100kmh-1.
    The horn is sounded for a short time.
    The frequency of the horn is 440Hz.
    An echo from the cliff is heard by the driver of the car and also by a stationary observer.
    If the speed of sound is 340ms-1, calculate the apparent frequency of the echo as perceived by:
  a) the stationary observer
b) the driver of the car.
17. It can be shown that the relative Doppler shift for electro-magnetic radiations like light, radio waves etc is given (approximately) by
where c is the speed of light and v is the relative speed of source and observer.
    The speed of a car is being measured by a police-person (please note the gender neutral tone of this question) using a "radar speed-measuring thing" (to give it its technical name).
    The frequency of the transmitted signal is 5GHz.
    When "mixed" the transmitted and received signals beat with a frequency of 750Hz.
    If the speed limit for the road is 110kmh-1, should the driver be fined or not?
18.   Plane waves on the surface of a liquid are generated by an oscillator of time period 0.1s and amplitude 2mm.
    The speed of propagation of the waves is 20cms-1.
  a) Calculate the wavelength
  b) At time t, point A (a point on the surface of the liquid near the oscillator) has displacement 2mm upwards.
    At time t, what will be the displacement of the following points:
    i)   point B, which is 7cm away from point A (measured along the direction of propagation of the waves)
    ii)  point C, which is 10.5cm away from point A (measured along the direction of propagation of the waves)
    iii) point D, which is 10cm away from point A (measured along the direction of propagation of the waves)
  c) Explain why your answers to parts b) i) and b) iii) above are approximate.
19.   The speed, v, of propagation of a wave along a string/spring/wire under tension depends on the tension, Te and the mass per unit length of the string/spring/wire, μ.
    Assuming that no other factors are involved, suggest a possible equation relating v, Te and μ.
    Explain how you arrived at the equation.
    You should be able to justify your suggestion by considering the units of the three quantities, v, Te and μ.
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