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1.
This question is about the interference of waves.
(a)
State the principle of superposition.
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(2)
A wire is stretched between two points A and B.
A
B
A standing wave is set up in the wire. This wave can be thought of as being made up from the
superposition of two waves, a wave X travelling from A to B and a wave Y travelling from B to
A. At one particular instant in time, the displacement of the wire is as shown. A background
grid is given for reference and the equilibrium position of the wire is shown as a dotted line.
A
B
1
(b)
On the grids below, draw the displacement of the wire due to wave X and wave Y.
Wave X
A
B
Wave Y
A
B
(4)
2
The diagram below shows an arrangement (not to scale) for observing the interference pattern
produced by the superposition of two light waves.
P
S1
monochromatic
light source
O
S
S2
single slit
double slit
Screen
S1 and S2 are two very narrow slits. The single slit S ensures that the light leaving the slits S1
and S2 is coherent.
(c)
(i)
Define coherent.
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(1)
(ii)
Explain why the slits S1 and S2 need to be very narrow.
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(2)
(Total 9 marks)
3
2.
The properties of sound waves
Reflection and Refraction
One method of finding the position of fish beneath a boat is to send out a pulse of sound waves
from the bottom of a boat and time how long the pulse takes to return as shown below. The
speed of sound waves in water is 1500 m s–1.
water
emitter and receiver
fish
(a)
The time between the pulse leaving the emitter and returning to the receiver is 12 ms.
Calculate the distance from the bottom of the boat to the fish.
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(2)
In order to find fish using this method, the effects of diffraction at the fish need to be
minimized.
(b)
(i)
The diagram below shows plane wavefronts incident on an obstacle. Complete the
diagram to show what is meant by diffraction of the wavefronts.
direction of
movement of
wavefronts
(2)
4
(ii)
Explain why you would expect the effects of diffraction to be negligible when
sound of frequency 60 kHz is incident on a large fish.
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(2)
The Doppler effect can be used to determine the speed of an object.
(c)
(i)
Explain what is meant by the Doppler effect.
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(2)
(ii)
A train approaches and then passes by a stationary observer. The train is moving
with constant velocity and emits a sound of constant frequency. The observer hears
the frequency change from 490 Hz to 410 Hz. The speed of sound in air is 340
m s–1. Estimate the speed of the train.
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(4)
(Total 12 marks)
5
3.
This question is about resolution.
(a)
State the Rayleigh criterion for the images of two point sources to be just resolved.
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(2)
A man is walking along a straight path at night towards two light sources as shown below.
light
sources
path
man
not drawn to scale
When the man is 150 m from the sources, the images of the two sources are just resolved by his
eye. The wavelength of the light from each source is 590 nm and the diameter of the aperture of
his eye is 5.0 mm.
(b)
Estimate the distance between the two sources.
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(3)
(Total 5 marks)
6
4.
This question is about some properties of waves associated with the principle of superposition.
Stationary (standing) waves and resonance
(a)
State two ways in which a standing wave differs from a continuous wave.
1.
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2.
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(2)
(b)
State the principle of superposition as applied to waves.
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(2)
(c)
A stretched string is fixed at one end. The other end is vibrated continuously to produce a
wave along the string. The wave is reflected at the fixed end and as a result a standing
wave is set up in the string.
The diagram below shows the displacement of the string at time t = 0. The dotted line
shows the equilibrium position of the string.
free end
fixed end
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(i)
The period of oscillation of the string is T. On the diagrams below, draw sketches
T
T
of the displacement of the string at time t  and at time t  .
2
4
t
T
4
t
T
2
(2)
(ii)
Use your sketches in (i) to explain why the wave in the string appears to be
stationary.
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(2)
8
(d)
Stationary waves are often associated with the phenomenon of resonance.
(i)
Describe what is meant by resonance.
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(2)
(ii)
On 19 September 1985 an earthquake occurred in Mexico City. Many buildings
that were about 80 m tall collapsed whereas buildings that were taller or shorter
than this remained undamaged. Use the data below to suggest a reason for this.
period oscillation of an 80 m tall building = 2.0 s
speed of earthquake waves
= 6.0  103 m s–1
average wavelength of the waves
= 1.2  104 m
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(3)
(Total 13 marks)
9
5.
This question is about diffraction.
Plane wavefronts of monochromatic light of wavelength  are incident on a rectangular slit of
width b. After passing through the slit, the light is brought to a focus on a screen distance D
from the slit as shown below. The width of the slit is comparable to the wavelength of the
incident light and b  D. The point P on the screen is opposite the centre of the slit.
b
P
D
slit
screen
The sketch graph below shows that the variation with angle  of the intensity of the light on the
screen.
intensity
 
10
(a)
Explain qualitatively, this intensity distribution.
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(3)
(b)
The angle  =  is the angular half-width of the central maximum of the intensity
λ
distribution and is given by the expression  = . Derive an expression in terms of D, 
b
and b for the half-width d of the central maximum.
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(2)
11
(c)
The single slit is replaced by two rectangular slits of width b. The distance between the
centre of the slits is equal to 2b.
On the axes below, draw a sketch of the intensity distribution on the screen. (The
intensity distribution of a single slit is shown by the dotted line.)
intensity
 
(2)
(Total 7 marks)
12