1. This question is about waves and wave properties.
(a) By making reference to waves, distinguish between a ray and a wavefront.
... ... ... ...
(3)
The diagram below shows three wavefronts incident on a boundary between medium I and medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete.
m e d i u m I
m e d i u m R A
B
C
D
E
F
(b) (i) On the diagram above, draw a line to complete the wavefront EF.
(1)
(ii) Explain in which medium, I or R, the wave has the higher speed.
... ... ... ...
(iii) By taking appropriate measurements from the diagram, determine the ratio of the speeds of the wave travelling from medium I to medium R.
... ... ...
(2)
The graph below shows the variation with time t of the velocity v of one particle of the medium
through which the wave is travelling. 8
6
4
2
0
– 2
– 4
– 6
– 8
0 1 2 3 4 5 6
t / m s
v / m s– 1
7
(c) (i) Explain how it can be deduced from the graph that the particle is oscillating.
... ... ...
(2)
(ii) Determine the frequency of oscillation of the particle.
... ...
(2)
(iii) Mark on the graph with the letter M one time at which the particle is at maximum displacement.
(1)
(iv) Estimate the area between the curve and the x-axis from the time t = 0 to the time
t = 1.5 ms.
... ...
(v) Suggest what the area in c (iv) represents.
...
(1) (Total 17 marks)
2. This question is about waves and wave properties.
The diagram below shows three wavefronts incident on a boundary between medium I and medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete.
m e d i u m I
m e d i u m R A
B
C
D
E
F
(a) (i) On the diagram above, draw a line to complete the wavefront EF.
(1)
(ii) Explain in which medium, I or R, the wave has the higher speed.
... ... ... ...
The graph below shows the variation with time t of the velocity v of one particle of the medium through which the wave is travelling.
8
6
4
2
0
– 2
– 4
– 6
– 8
0 1 2 3 4 5 6
t / m s
v / m s– 1
7
(b) (i) Explain how it can be deduced from the graph that the particle is oscillating.
... ... ...
(2)
(ii) Determine the frequency of oscillation of the particle.
... ...
(2)
(iii) Mark on the graph with the letter M one time at which the particle is at maximum displacement.
(1)
(iv) Estimate the area between the curve and the x-axis from the time t = 0 to the time
t = 1.5 ms.
... ...
(2)
(v) Suggest what the area in b (iv) represents.
...
(c) (i) State the principle of superposition.
... ...
(2)
Two loudspeakers S1 and S2 are connected to the same output of a frequency generator and are
placed in a large room as shown below.
S S
2 1
5 6 0 c m
5 8 0 c m
5 5 0 c m
P
M
Sound waves of wavelength 40 cm and amplitude A are emitted by both loudspeakers.
M is a point distance 550 cm from both S1 and S2. Point P is a distance 560 cm from S1 and
580 cm from S2.
(ii) State and explain what happens to the loudness of the sound detected by a
microphone when the microphone is moved from point M to point P.
... ... ... ... ...
(4)
(iii) Referring to the diagram above, the amplitude of the wave emitted by S1 is now
increased to 2A. The wave emitted by S2 is unchanged. Deduce what change, if any,
occurs in the loudness of the sound at point M and at point P when this change in amplitude is made.
(iv) The loudspeakers are now replaced with two monochromatic light sources. State the reason why bright and dark fringes are not observed along the line PM. ...
(1)
Waves of frequency f and speed c are emitted by a stationary source of sound. An observer
moves along a straight line towards the source at a constant speed v.
(d) State, in terms of f, c and v, an expression for
(i) the wavelength of the sound detected by the observer.
...
(1)
(ii) the apparent speed of the wave as measured by the observer.
...
(1) (Total 25 marks)
3. This question is about waves and wave properties.
Travelling and standing (stationary) waves
(a) State two differences between a travelling wave and a standing (stationary) wave.
1. ... ... 2. ... ...
(b) In the scale diagram below, plane wavefronts travel from medium 1 to medium 2 across the boundary AB.
d i r e c t i o n o f t r a v e l
m e d i u m 1
A B
m e d i u m 2
State and explain in which medium the wavefronts have the greater speed. ... ... ... ...
(3)
(c) By taking measurements from the diagram, determine the ratio
. 2 medium in
wave of speed
1 medium in
wave of speed
... ... ... ...
(d) To demonstrate the production of a standing wave, Samantha attaches the end B of a length AB of rubber tubing to a rigid support. She holds the other end A of the tubing, pulls on it slightly and then shakes the end A in a direction at right angles to AB. At a certain frequency of shaking, the tubing is seen to form the standing wave pattern shown below.
A B
Explain how this pattern is formed.
... ... ... ... ... ...
(5)
(e) The speed v with which energy is propagated in the tubing by a travelling wave depends
on the tension T in the tubing. The relationship between these quantities is
T k v
where k is a constant.
In an experiment to verify this relationship, the fundamental (first harmonic) frequency f
was measured for different values of tension T.
(i) Explain how the results of this experiment, represented graphically, can be used to
verify the relationship vk T.
... ... ... ... ... ...
(4)
fundamental frequency for a tension of 9.0 N in the tubing was 1.8 Hz. Calculate
the numerical value of the constant k.
... ... ... ... ...
(3)
The Doppler effect
(f) A source S emits sound waves at constant frequency. In the diagram below, S is moving at
constant speed in the direction shown, along a straight-line between two stationary observers A and B.
B A
S
(i) Draw, on the above diagram, three wavefronts representing the waves emitted by S.
(2)
(ii) Use your sketch to explain any difference in the frequency of the sound as heard by
observer A and by observer B.
... ... ... ...
4. This question is about wave phenomena and the particle nature of light. Travelling waves
(a) Graph 1 below shows the variation with time t of the displacement d of a travelling
(progressive) wave. Graph 2 shows the variation with distance x along the same wave of
its displacement d.
t / s
x / c m 4 2 0 – 2 – 4 4 2 0 – 2 – 4
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6
2 . 4 2 . 0
1 . 6 1 . 2
0 . 8 0 . 4
0 . 0 G r a p h 1
d / m m
G r a p h 2
d / m m
(i) State what is meant by a travelling wave.
... ...
(1)
(ii) Use the graphs to determine the amplitude, wavelength, frequency and speed of the
Refraction of waves
(b) The diagram below shows plane wavefronts incident on a boundary between two media A
and B.
m e d i u m A m e d i u m B
The ratio is1.4.
A medium of
index refractive
B medium of
index refractive
The angle between an incident wavefront and the normal to the boundary is 50.
(i) Calculate the angle between a refracted wavefront and the normal to the boundary.
... ... ... ...
(3)
(ii) On the diagram above, construct three wavefronts to show the refraction of the
wave at the boundary.
(3)
Interference of waves
(c) State two conditions necessary to produce observable interference between light from two
sources.
1. ... 2. ...
(d) A Young’s double slit experiment for red light is set up as shown below.
s o u r c e o f w h i t e l i g h t
r e d f i l t e r d o u b l e s l i t
s i n g l e s l i t
s c r e e n
( n o t t o s c a l e )
An interference pattern of light and dark fringes is observed on the screen.
(i) The red filter is now replaced by a blue filter. State and explain the change in
appearance, other than change of colour, of the fringes on the screen. ... ... ...
(2)
(ii) The filter in (i) is removed. State and explain the appearance of the central
maximum fringe and also of fringes that are away from this central position. ... ... ... ... ...
Particle nature of light
(e) The photo-electric effect cannot be explained on the basis of a wave theory of
electromagnetic radiation. State two experimental observations, other than the existence of a threshold frequency, that led to this conclusion.
1. ... ... 2. ... ...
(2)
(f) Monochromatic light is incident on a metal surface in a photo-cell as shown below.
μA
m o n o c h r o m a t i c l i g h t
The metal surface has work function 2.4 eV and the threshold wavelength for light
incident on the surface is S. The current in the photo-cell is measured using a
microammeter.
Calculate the threshold wavelength S.
... ... ... ...
(g) Light of wavelength 21
λ
S and intensity I is incident on the metal surface in (f). (Intensityis the light power incident per unit area.) The current in the photo-cell is iP.
State and explain the effect on the current iP in the photo-cell for light incident on the
surface
(i) of wavelength 12
λ
Sand intensity 2I;... ... ...
(3)
(ii) of wavelength less than 21
λ
Sand intensity I.... ... ...
(3) (Total 30 marks)
5. Wave properties
(a) By reference to the energy of a travelling wave, state what is meant by
(i) a ray.
... ...
(1)
(ii) wave speed.
... ...
(b) The graph below shows the variation with time t of the displacement xA of wave A as it passes through a point P.
3 . 0
2 . 0
1 . 0
0 . 0
– 1 . 0
– 2 . 0
– 3 . 0
1 0 . 0 8 . 0
6 . 0 4 . 0
2 . 0
0 . 0 t / m s
x A/ m m
W a v e A
The graph below shows the variation with time t of the displacement xB of wave B as it
passes through point P.
2 . 0
1 . 0
0 . 0
– 1 . 0
– 2 . 0
1 0 . 0 8 . 0
6 . 0 4 . 0
2 . 0
0 . 0 t / m s
x B/ m m
W a v e B
(i) Calculate the frequency of the waves.
... ...
(1)
(ii) The waves pass simultaneously through point P. Use the graphs to determine the
resultant displacement at point P of the two waves at time t = 1.0 ms and at time t =
8.0 ms.
At t = 1.0 ms: ... ... At t = 8.0 ms: ... ...
6. 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 bD. The point P on the screen is opposite the centre of the slit.
P
s c r e e n s l i t
D b
The sketch graph below shows that the variation with angle
of the intensity of the light on thescreen.
i n t e n s i t y
(a) Explain qualitatively, this intensity distribution.
... ... ... ... ...
(3)
(b) The angle
=
is the angular half-width of the central maximum of the intensitydistribution and is given by the expression
= .b λ
Derive an expression in terms of D,
and b for the half-width d of the central maximum.
... ... ...
(2)
(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.)
i n t e n s i t y
