1
The least distance between two points of a progressive transverse wave which have a phase
difference of
wave?
rad is 0.050 m. If the frequency of the wave is 500 Hz, what is the speed of the
A
25 m s–1
B
75 m s–1
C
150 m s–1
D
1666 m s–1
(Total 1 mark)
2
The diagram below is an arrangement for analysing the light emitted by a source.
(a)
Suggest a light source that would emit a continuous spectrum.
........................................................................................................................
(1)
(b)
The light source emits a range of wavelengths from 500 nm to 700 nm. The light is incident
on a diffraction grating that has 10 000 lines per metre.
(i)
Calculate the angle from the straight through direction at which the first order
maximum for the 500 nm wavelength is formed.
Angle = ........................................
(3)
(ii)
Calculate the angular width of the first order spectrum.
Angular width ........................................
(1)
(iii)
The detector is positioned 2.0 m from the grating. Calculate the distance between the
extreme ends of the first order spectrum in this position.
Distance = ........................................
(1)
Page 1 of 64
(c)
The single slit is initially illuminated by light from a point source that is 0.02 m from the slit.
State and explain how the intensity of light incident on the single slit changes when the light
source is moved to a position 0.05 m from the slit.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(4)
(Total 10 marks)
3
Monochromatic light passes from air into water. Which one of the following statements is true?
A
The velocity, frequency and wavelength all change
B
The velocity and frequency change but not the wavelength
C
The velocity and wavelength change but not the frequency
D
The frequency and wavelength change but not the velocity
(Total 1 mark)
4
Two waves with amplitudes a and 3a interfere.
The ratio
A
2
B
3
C
4
D
infinity
is
(Total 1 mark)
5
The intensity of a sound is 1.9 × 10–8 W m–2 at a distance of 0.25 km from the source. Calculate
the intensity of the sound at a distance of 0.75 km from the source.
Intensity of sound ....................................
(Total 3 marks)
Page 2 of 64
6
Short pulses of sound are reflected from the wall of a building 18 m away from the sound source.
The reflected pulses return to the source after 0.11 s.
(a)
Calculate the speed of sound.
Speed of sound ........................................
(3)
(b)
The sound source now emits a continuous tone at a constant frequency. An observer,
walking at a constant speed from the source to the wall, hears a regular rise and fall in the
intensity of the sound. Explain how the minima of intensity occur.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 6 marks)
Page 3 of 64
7
The diagram below shows three wavefronts of light directed towards a glass block in the air. The
direction of travel of these wavefronts is also shown.
Complete the diagram to show the position of these three wavefronts after partial reflection and
refraction at the surface of the glass block.
(Total 3 marks)
8
(a)
Figure 1 shows how the displacement s of the particles in a medium carrying a pulse of
ultrasound varies with distance d along the medium at one instant.
Figure 1
(i)
State the amplitude of the wave.
...............................................................................................................
(1)
Page 4 of 64
(ii)
The speed of the wave is 1200 m s–1. Calculate the frequency of oscillation of the
particles of the medium when the ultrasound wave is travelling through it.
Frequency of oscillation ..........................................
(3)
(b)
An ultrasound transmitter is placed directly on the skin of a patient. Figure 2 shows the
amplitudes of the transmitted pulse and the pulse received after reflection by an organ in
the body. amplitude
Figure 2
(i)
Give two possible reasons why the amplitude of the received pulse is lower than that
which is transmitted.
Reason 1 ..............................................................................................
...............................................................................................................
Reason 2 ..............................................................................................
...............................................................................................................
(2)
(ii)
The speed of ultrasound in body tissue is 1200 m s–1. Calculate the depth of the
reflecting surface below the skin.
Depth of reflecting surface ......................................
(2)
(Total 8 marks)
Page 5 of 64
9
The diagram below shows a hammer being struck against the end of a horizontal metal rod. A
pulse of sound travels along the rod from where the hammer strikes it to the far end and back
again. The sound pulse throws the hammer and rod apart when it returns. An electrical timing
circuit measures the time for which the hammer and the rod are in contact.
(a)
Circle the word below that describes the type of wave that travels along the rod.
transverse
longitudinal
(1)
(b)
State the name of the effect that causes the sound pulse to return to the hammer.
........................................................................................................................
(1)
(c)
The rod is 0.45 m long and the time for which the hammer is in contact with the rod is
1.6 × 10–4 s. Calculate the speed of sound in the rod.
Speed of sound ...................................................
(3)
(Total 5 marks)
Page 6 of 64
10
A square metre of the Moon’s surface that is perpendicular to sunlight receives 1.4 kJ of energy
every second from the Sun. Estimate the total energy radiated by the Sun every second
assuming that the Sun acts as a point source.
mean distance of the Moon from the Sun = 1.5 × 1011 m
Total energy radiated .........................................
(Total 3 marks)
11
(a)
With the aid of a clearly labelled diagram explain how a sound wave in air transmits energy
away from its source.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
Page 7 of 64
(b)
Unlike sound waves, transverse waves can be polarised. Give one example of a
transverse wave and draw a diagram to show how it can be plane polarised. State a
method of polarising a wave of the type you have chosen.
Example transverse wave ........................................
Method of polarisation .......................................................
(3)
(Total 6 marks)
Page 8 of 64
12
The graph in Figure 1 shows the results of an investigation of how the visible light intensity
I varies with distance d from a filament lamp. The lamp can be assumed to behave as a point
source of light.
Figure 1
(a)
Use data from the graph to show that the visible light intensity varies with distance
according to an inverse square law.
(3)
(b)
Find the power of the visible light emitted by the filament lamp.
power ..........................................
(2)
(Total 5 marks)
Page 9 of 64
13
Figure 1 shows three particles in a medium that is transmitting a sound wave. Particles A and C
are separated by one wavelength and particle B is half way between them when no sound is
being transmitted.
Figure 1
(a)
Name the type of wave that is involved in the transmission of this sound.
........................................................................................................................
(1)
(b)
At one instant particle A is displaced to the point A' indicated by the tip of the arrow in
Figure 1. Show on Figure 1 the displacements of particles B and C at the same instant.
Label the position B' and C' respectively.
(1)
(c)
Explain briefly how energy is transmitted in this sound wave.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(Total 4 marks)
Page 10 of 64
14
Figure 1 shows the displacement of particles in an ultrasound wave at different distances from
the source at a particular time. The wave travels at 3200 m s–1.
Figure 1
(a)
(i)
Use the graph to find the wavelength of the wave in Figure 1.
wavelength .........................................
(ii)
Calculate the frequency of the ultrasound wave.
frequency ...........................................
(3)
Page 11 of 64
(b)
One industrial use for ultrasound waves is to detect flaws inside a metal block. Figure 2a
shows the arrangement in which the waves are fired downwards in short pulses from a
transmitter. Figure 2b shows the amplitudes of the initial pulse and the reflected signals
recorded by the receiver. You may assume that there is no reflected pulse received from
the upper surface of the block.
Figure 2a
Figure 2b
Page 12 of 64
The ultrasound wave travels at 3200 m s–1. Use data from Figure 2b to calculate the
distance of the flaw below the top of the block.
distance ................................
(3)
(Total 6 marks)
15
A source emits light of wavelength 600 nm as a train of waves lasting 0.01 µs. How many
complete waves are sent out?
speed of light = 3 × 108 m s−1
A
5 × 106
B
18 × 107
C
5 × 109
D
5 × 1022
(Total 1 mark)
16
Explain the differences between an undamped progressive transverse wave and a stationary
transverse wave, in terms of (a) amplitude, (b) phase and (c) energy transfer.
(a)
amplitude
progressive wave ...........................................................................................
........................................................................................................................
stationary wave ..............................................................................................
........................................................................................................................
(b)
phase
progressive wave ...........................................................................................
........................................................................................................................
stationary wave ..............................................................................................
........................................................................................................................
Page 13 of 64
(c)
energy transfer
progressive wave ...........................................................................................
........................................................................................................................
stationary wave ..............................................................................................
........................................................................................................................
(Total 5 marks)
17
(a)
For a sound wave travelling through air, explain what is meant by particle displacement,
amplitude and wavelength.
Particle displacement ....................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
amplitude .......................................................................................................
........................................................................................................................
.......................................................................................................................
wavelength .....................................................................................................
........................................................................................................................
........................................................................................................................
(4)
Page 14 of 64
(b)
Graph A shows the variation of particle displacement with time at a point on the path of a
progressive wave of constant amplitude.
Graph B shows the variation of particle displacement with distance along the same wave
at a particular instant.
(i)
Show on graph A
(1) the wave amplitude, a,
(2) the period, T, of the vibrations providing the wave.
(ii)
Show on graph B
(1) the wavelength of the wave, λ,
(2) two points, P and Q, which are always π/2 out of phase.
(4)
(Total 8 marks)
18
A progressive wave in a stretched string has a speed of 20 m s−1 and a frequency of 100 Hz.
What is the phase difference between two points 25 mm apart?
A
zero
B
rad
C
rad
D
π rad
(Total 1 mark)
19
A wave motion has period T, frequency f, wavelength λ and speed ʋ. Which one of the following
equations is incorrect?
Page 15 of 64
A
1 = Tf
B
T=
C
λ=
D
Tʋ = λ
(Total 1 mark)
20
(a)
The diagram shows the apparatus required for a simple experiment to measure the speed
of sound.
A pulse of sound is sent down a hollow glass tube and is reflected at the sealed end of the
tube. A microphone, M, placed at the open end detects the initial pulse and, at a later time,
the reflected pulse. The microphone is connected to an oscilloscope which gives a signal
when the microphone detects a pulse of sound.
The signal displayed on the oscilloscope screen is shown below.
If the time base of the oscilloscope is set to 2.0 ms per division, estimate the speed of
sound in air.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
Page 16 of 64
(b)
Describe how the frequency of a sinusoidal alternating (ac) voltage source is measured
using an oscilloscope.
Your answer should include a sketch of the trace seen on the oscilloscope screen and
explain how the frequency is obtained from this trace.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(5)
(Total 8 marks)
21
The audible range of a girl's hearing is 30 Hz to 16 500 Hz. If the speed of sound in air is 330 m
s−1, what is the shortest wavelength of sound in air which the girl can hear?
A
m
B
m
C
m
D
m
(Total 1 mark)
Page 17 of 64
22
displacement
The graph shows, at a particular instant, the variation of the displacement of the particles in a
transverse progressive water wave, of wavelength 4 cm, travelling from left to right. Which one of
the following statements is not true?
A
The distance PS = 3 cm.
B
The particle velocity at Q is a maximum.
C
The particle at S is moving downwards
D
Particles at P and R are in phase.
(Total 1 mark)
23
Two points on a progressive wave are one-eighth of a wavelength apart. The distance between
them is 0.5 m, and the frequency of the oscillation is 10 Hz. What is the minimum speed of the
wave?
A
0.2 m s–1
B
10 m s–1
C
20 m s–1
D
40 m s–1
(Total 1 mark)
Page 18 of 64
A wave of frequency 5 Hz travels at 8 km s
24
–1
through a medium. What is the phase difference, in
radians, between two points 2 km apart?
A0
B
Cπ
D
(Total 1 mark)
25
Which line, A to D, in the table gives a correct difference between a progressive wave and a
stationary wave?
progressive wave
stationary wave
all the particles vibrate
some of the particles do not
vibrate
B
none of the particles vibrate
with the same amplitude
all the particles vibrate with
the same amplitude
C
all the particles vibrate in
phase with each other
none of the particles vibrate in
phase with each other
D
some of the particles do not
vibrate
all the particles vibrate in
phase with each other
A
(Total 1 mark)
26
Two points on a progressive wave differ in phase by . The distance between them is 0.5 m,
and the frequency of the oscillation is 10 Hz. What is the minimum speed of the wave?
A
0.2 m s−1
C
10 m s−1
C
20 m s−1
D
40 m s−1
(Total 1 mark)
Page 19 of 64
27
The speed of sound in water is 1500 m s−1. For a sound wave in water having frequency 2500
Hz, what is the minimum distance between two points at which the vibrations are
phase?
A
0.05 m
B
0.10 m
C
0.15 m
D
0.20 m
rad out of
(Total 1 mark)
28
The diagram shows a snapshot of a wave on a rope travelling from left to right.
At the instant shown, point P is at maximum displacement and point Q is at zero displacement.
Which one of the following lines, A to D, in the table correctly describes the motion of P and Q in
the next half-cycle?
P
Q
A
falls then rises
rises
B
falls then rises
rises then falls
C
falls
falls
D
falls
rises then falls
(Total 1 mark)
Page 20 of 64
29
An aerial system consists of a horizontal copper wire of length 38 m supported between two
masts, as shown in the figure below. The wire transmits electromagnetic waves when an
alternating potential is applied to it at one end.
(a)
The wavelength of the radiation transmitted from the wire is twice the length of the copper
wire. Calculate the frequency of the transmitted radiation.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(1)
(b)
The ends of the copper wire are fixed to masts of height 12.0 m. The masts are held in a
vertical position by cables, labelled P and Q, as shown in the figure above.
(i)
P has a length of 14.0 m and the tension in it is 110 N. Calculate the tension in the
copper wire.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
The copper wire has a diameter of 4.0 mm. Calculate the stress in the copper wire.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
Page 21 of 64
(iii)
Discuss whether the wire is in danger of breaking if it is stretched further due to
movement of the top of the masts in strong winds.
breaking stress of copper = 3.0 × 108 Pa
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(7)
(Total 8 marks)
30
(a)
The diagram below represents a progressive wave travelling from left to right on a
stretched string.
(i)
Calculate the wavelength of the wave.
answer ................................... m
(1)
(ii)
The frequency of the wave is 22 Hz. Calculate the speed of the wave.
answer............................m s–1
(2)
Page 22 of 64
(iii)
State the phase difference between points X and Y on the string, giving an
appropriate unit.
answer ..............................
(2)
(b)
Describe how the displacement of point Y on the string varies in the next half-period.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 7 marks)
31
Figure 1 shows a side view of a string on a guitar. The string cannot move at either of the two
bridges when it is vibrating. When vibrating in its fundamental mode the frequency of the sound
produced is 108 Hz.
(a)
(i)
On Figure 1, sketch the stationary wave produced when the string is vibrating in its
fundamental mode.
Figure 1
(1)
Page 23 of 64
(ii)
Calculate the wavelength of the fundamental mode of vibration.
answer = ........................................... m
(2)
(iii)
Calculate the speed of a progressive wave on this string.
answer = ...................................... m s–1
(2)
(b)
While tuning the guitar, the guitarist produces an overtone that has a node 0.16 m from
bridge A.
(i)
On Figure 2, sketch the stationary wave produced and label all nodes that are
present.
Figure 2
(2)
(ii)
Calculate the frequency of the overtone.
answer = ...................................... Hz
(1)
Page 24 of 64
(c)
The guitarist needs to raise the fundamental frequency of vibration of this string.
State one way in which this can be achieved.
......................................................................................................................
......................................................................................................................
(1)
(Total 9 marks)
32
(a)
Define the amplitude of a wave.
......................................................................................................................
......................................................................................................................
(1)
(b)
(i)
Other than electromagnetic radiation, give one example of a wave that is transverse.
.............................................................................................................
(1)
(ii)
State one difference between a transverse wave and a longitudinal wave.
.............................................................................................................
.............................................................................................................
(1)
(c)
The figure below shows two identical polarising filters, A and B, and an unpolarised light
source. The arrows indicate the plane in which the electric field of the wave oscillates.
(i)
If polarised light is reaching the observer, draw the direction of the transmission axis
on filter B in the figure below.
(1)
Page 25 of 64
(ii)
The polarising filter B is rotated clockwise through 360º about line XY from the
position shown in the figure above. On the axes below, sketch how the light intensity
reaching the observer varies as this is done.
(2)
(d)
State one application, other than in education, of a polarising filter and give a reason for its
use.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 8 marks)
33
The figure below shows a continuous progressive wave on a rope. There is a knot in the rope.
(a)
Define the amplitude of a wave.
........................................................................................................................
........................................................................................................................
(2)
Page 26 of 64
(b)
The wave travels to the right.
Describe how the vertical displacement of the knot varies over the next complete cycle.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(c)
A continuous wave of the same amplitude and frequency moves along the rope from the
right and passes through the first wave. The knot becomes motionless.
Explain how this could happen.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 8 marks)
Page 27 of 64
34
The figure below shows two ways in which a wave can travel along a slinky spring.
(a)
State and explain which wave is longitudinal.
........................................................................................................................
........................................................................................................................
(2)
(b)
On the figure above,
(i)
clearly indicate and label the wavelength of wave B
(1)
(ii)
use arrows to show the direction in which the points P and Q are about to move as
each wave moves to the right.
(2)
(c)
Electromagnetic waves are similar in nature to wave A.
Explain why it is important to correctly align the aerial of a TV in order to receive the
strongest signal.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(Total 7 marks)
Page 28 of 64
35
When a note is played on a violin, the sound it produces consists of the fundamental and many
overtones.
Figure 1 shows the shape of the string for a stationary wave that corresponds to one of these
overtones. The positions of maximum and zero displacement for one overtone are shown. Points
A and B are fixed. Points X, Y and Z are points on the string.
Figure 1
(a)
(i)
Describe the motion of point X.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
(2)
(ii)
State the phase relationship between
X and Y .................................................................................................
X and Z .................................................................................................
(2)
(b)
The frequency of this overtone is 780 Hz.
(i)
Show that the speed of a progressive wave on this string is about 125 ms–1.
(2)
(ii)
Calculate the time taken for the string at point Z to move from maximum displacement
back to zero displacement.
answer = ................................... s
(3)
Page 29 of 64
(c)
The violinist presses on the string at C to shorten the part of the string that vibrates.
Figure 2 shows the string between C and B vibrating in its fundamental mode. The length
of the whole string is 320 mm and the distance between C and B is 240 mm.
Figure 2
(i)
State the name given to the point on the wave midway between C and B.
...............................................................................................................
(1)
(ii)
Calculate the wavelength of this stationary wave.
answer = ................................... m
(2)
(iii)
Calculate the frequency of this fundamental mode. The speed of the progressive
wave remains at 125 ms–1.
answer = .................................Hz
(1)
(Total 13 marks)
Page 30 of 64
36
Earthquakes produce transverse and longitudinal seismic waves that travel through rock. The
diagram below shows the displacement of the particles of rock at a given instant, for different
positions along a transverse wave.
(a)
State the phase difference between
(i)
points A and B on the wave ...................................................................
(ii)
points A and C on the wave ...................................................................
(2)
(b)
Describe the motion of the rock particle at point B during the passage of the next complete
cycle.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(c)
A scientist detects a seismic wave that is polarised. State and explain what the scientist
can deduce from this information.
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
Page 31 of 64
(d)
The frequency of the seismic wave is measured to be 6.0 Hz.
(i)
Define the frequency of a progressive wave.
...............................................................................................................
...............................................................................................................
(1)
(ii)
Calculate the wavelength of the wave if its speed is 4.5 × 103 m s–1.
wavelength .......................................... m
(2)
(Total 9 marks)
37
Ultrasound waves are used to produce images of a fetus inside a womb.
(a)
Explain what is meant by the frequency of a wave.
........................................................................................................................
........................................................................................................................
........................................................................................................................
(1)
(b)
Ultrasound is a longitudinal wave. Describe the nature of a longitudinal wave.
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(c)
In order to produce an image with sufficient detail, the wavelength of the ultrasound must
be 0.50 mm. The speed of the ultrasound in body tissue is 1540 m s–1. Calculate the
frequency of the ultrasound at this wavelength.
Give your answer to an appropriate number of significant figures.
frequency ........................................ Hz
(2)
Page 32 of 64
(d)
A continuous ultrasound wave of constant frequency is reflected from a solid surface and
returns in the direction it came from.
Assuming there is no significant loss in amplitude upon reflection, describe and explain the
effect the waves have on the particles in the medium between the transmitter and the solid
surface.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 8 marks)
Page 33 of 64
38
The diagram shows two pulses on a string travelling towards each other.
Which of the following diagrams shows the shape of the string when the pulses have passed
through each other?
A
B
C
D
(Total 1 mark)
39
Sound waves cross a boundary between two media X and Y. The frequency of the waves in X is
400 Hz. The speed of the waves in X is 330 m s–1 and the speed of the waves in Y is 1320 m s–1.
What are the correct frequency and wavelength in Y?
Frequency / Hz
Wavelength / m
A
100
0.82
B
400
0.82
C
400
3.3
D
1600
3.3
(Total 1 mark)
Page 34 of 64
40
Read through the following passage and answer the questions that follow it.
Measuring the speed of sound in air
5
10
(a)
After the wave nature of sound had been identified, many attempts were made to
measure its speed in air. The earliest known attempt was made by the French
scientist Gassendi in the 17th century. The procedure involved timing the interval
between seeing the flash of a gun and hearing the bang from some distance away.
Gassendi assumed that, compared with the speed of sound, the speed of light is
infinite. The value he obtained for the speed of sound was 480 m s–1. He also
realised that the speed of sound does not depend on frequency.
A much better value of 350 m s–1 was obtained by the Italian physicists Borelli and
Viviani using the same procedure. In 1740 another Italian, Bianconi, showed that
sound travels faster when the temperature of the air is greater.
In 1738 a value of 332 m s–1 was obtained by scientists in Paris. This is remarkably
close to the currently accepted value considering the measuring equipment
available to the scientists at that time. Since 1986 the accepted value has been
331.29 m s–1 at 0 °C.
Suggest an experiment that will demonstrate the wave nature of sound (line 1).
........................................................................................................................
........................................................................................................................
........................................................................................................................
(1)
(b)
Using Gassendi’s value for the speed of sound (line 6), calculate the time between seeing
the flash of a gun and hearing its bang over a distance of 2.5 km.
time = ........................ s
(1)
(c)
Explain why it was necessary to assume that ‘compared with the speed of sound, the
speed of light is infinite’ (line 5).
........................................................................................................................
........................................................................................................................
........................................................................................................................
(1)
Page 35 of 64
(d)
Explain one observation that could have led Gassendi to conclude that ‘the speed of sound
does not depend on frequency’ (line 7).
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(e)
Explain how the value obtained by Borelli and Viviani was ‘much better’ than that obtained
by Gassendi (line 8).
........................................................................................................................
........................................................................................................................
(1)
(f)
The speed of sound c in dry air is given by
where θ is the temperature in °C, and k is a constant.
Calculate a value for k using data from the passage.
k = ........................ m s–1 K–½
(2)
(g)
State the steps taken by the scientific community for the value of a quantity to be ‘accepted’
(line 13).
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(Total 10 marks)
Page 36 of 64
Mark schemes
1
2
C
[1]
(a)
filament lamp / sun etc.
B1
(1)
(b)
(i)
d = 1.0 × 10–4 m
C1
use of λ = dsin θ or substituted values
C1
θ1 = 0.286° / 0.29°
A1
(3)
(ii)
Δθ = 0.115° (c.a.o.)
B1
(1)
(iii)
width = 4.0 × 10–3 m or 3.9 × 10–3 m (e.c.f. for 2 × sin (b(ii))
or 2 × tan (b(ii)); allow 1 s.f.)
B1
(1)
(c)
lower intensity
C1
because energy spreads
C1
use or statement of inverse square law
C1
ratio 0.16 or falls by factor of 6.25 c.a.o.
A1
(4)
[10]
3
4
5
C
[1]
A
[1]
use of inverse-square law
C1
3 × distance so 1 / 9 × intensity (or equivalent calc)
C1
1.9 × 10–8 / 9 = 2.11 × 10–9 Wm–2
A1
[3]
Page 37 of 64
6
(a)
distance travelled = 2 × 18 m
C1
Speed = 36 / 0.11
M1
= 327 m / s [164 m / s scores 2]
A1
(b)
mention of standing waves or superposition or interference
B1
mention of two waves, opposite directions
B1
because they are permanently out of phase, permanently
destructively interfere, permanently in antiphase
B1
[6]
7
reflection wavefront direction sensible
B1
refraction wavefront direction sensible
B1
one pair of wavefronts correctly spaced
B1
[3]
8
(a)
(i)
2(.0) × 10–5 m (i.e. allow 1 sf)
B1
1
(ii)
λ = 4(.0) × 10–4 (m)
B1
v = fλ (condone c = fλ)
C1
3.0 MHz sf penalty applies
allow e.c.f. for omitting 10–4 (300 Hz) but sf penalty
applies for e.g. 0.3 kHz)
A1
3
Page 38 of 64
(b)
(i)
ultrasound/wave/pulse/energy spreads out from
the transmitter (beam not uni-directional)
B1
energy is absorbed by(or lost to) the transmitting
medium/tissue/body
B1
incident ultrasound/wave/pulse/energy is not all
reflected (by the reflecting object)
or some is transmitted /absorbed by the organ
or is reflected at different angles (so does not return
to detector)
B1
some ultrasound/wave/pulse/energy reflected by the
skin since gel was not used
B1
max2
ANY 2
(ii)
distance travelled 1200 × 95 or 114 000 or 0.114 m
(i.e. mark for use of velocity × time ignoring powers
of 10)
C1
0.057 m ( allow answers in range 0.055 to 0.057 )
A1
2
[8]
Page 39 of 64
9
(a)
longitudinal
B1
(b)
reflection
B1
(c)
use of speed = distance/time
C1
(0.45 or 0.9)/1.6 × 10–4 or 0.45/0.8 × 10–4
C1
= 5.6 km s-1 [5.625]
A1
[5]
10
use of r2
C1
P = 1.4 × 103 × 4 × 3.14 × (1.5 × 1011)2
C1
= 3.96 × 1026 W
A1
[3]
Page 40 of 64
11
(a)
Good diagram of pressure variations/particle oscillations
with at least one label indicating direction of propagation,
pressure variation or density variation
B1
Plus any two from five of
Vibrating source
B1
Energy transferred to (air) molecules
B1
Energy passed on by collisions between molecules
B1
Oscillations of air molecule neighbours slightly out
of phase
B1
Oscillations/waves are longitudinal/energy transfer parallel
to vibrations
B1
3
(b)
Diagram showing several transverse vibrations/waves which are
subsequently limited to one after polarisation
B1
Valid example (light, microwaves etc.)
accept sunlight
Suitable polariser for the stated example
M1
(polaroid, reflection, metal grid etc). Not sunglasses
A1
3
[6]
Page 41 of 64
12
(a)
Statement that Id2 (or Ir2) should be constant
C1
Calculation of Id2 for two corresponding values of I and d
C1
Calculation of Id2 for three corresponding values of I and d
with conclusion
A1
3
or
work out constant for one set
C1
Calculate intensity for 1 new distance
C1
Calculate intensity for 2 new distances and compares with
graph.
A1
or
Reads one value from graph and calculates value for double
distance
C1
Explains that this is ¼ original intensity
C1
Does this twice with conclusion
A1
(b)
I = P/4πd2 or substitution of two corresponding values of I
and d
C1
0.40 W (condone 1sf)
A1
2
[5]
Page 42 of 64
13
(a)
longitudinal wave
B1
1
(b)
arrows showing B displaced to the left and C to the right
B1
1
(c)
particles in the transmitting medium are made to vibrate/given
energy
B1
or
mention of a compression/region of increased pressure (or
rarefaction)
cause nearby particles to vibrate/have energy/move
B1
or
the compression produces a compression further along (the
medium)
2
[4]
14
(a)
(i)
wavelength read-off = 1.2 mm
B1
(ii)
3200/1.2 × 10-3 ecf from (a) (i)
C1
3
2.7 MHz
A1
Page 43 of 64
(b)
read-off correct 1.3 µs
C1
factor of two correct
C1
3
= 2.1 × 10-3 m [2.08] c.a.o.
A1
[6]
15
16
A
[1]
amplitude:
each point along wave (1)
has same amplitude for progressive wave
but varies for stationary wave (1)
phase:
progressive wave, adjacent points vibrate with different phase (1)
stationary wave, between nodes all particles vibrate in phase
[or there are only two phases] (1)
energy transfer:
progressive wave, energy is transferred through space (1)
stationary wave, energy is not transferred through space (1)
[5]
17
(a)
(i)
displacement is distance of particle (1)
from mean [or equilibrium] position (1)
in direction of wave (energy) (1)
amplitude is maximum displacement (1)
wavelength is shortest distance (1)
between two points in phase (1)
(max 4)
Page 44 of 64
(b)
any two points
apart (1)
(4)
[8]
18
19
20
B
[1]
B
[1]
(a)
time elapsed = 8.5 ± 0.2 (ms) (1)
distance travelled = 3 (m) (1)
(allow C.E. if d = 1.5 (m))
speed of sound =
= 350 m s–1 (353) (1)
3
(b)
connect oscilloscope across ac source (or diagram or ac to Y plates) (1)
adjust time base to give trace (1)
adjust voltage sensitivity (1)
sinusoidal trace shown (1)
how to measure T from trace (1)
max 5
[8]
Page 45 of 64
21
22
23
24
25
26
27
28
29
C
[1]
D
[1]
D
[1]
B
[1]
A
[1]
D
[1]
B
[1]
D
[1]
(a)
λ(=2 × 38) = 76(m)
MHz (1)
1
(b)
(i)
angle between cable and horizontal =
(1)
T= 110 cos59° = 57N • (56.7N) (1)
(allow C.E. for value of angle)
(ii)
cross-sectional area (= P(2.0 × 10–3)2)
=1.3 × 10–5(m2) (1)
(1.26 × 10–5(m2))
stress
(1)
= 4.4 × 106Pa (1)
(4.38 × 106Pa)
(use of 56.7 and 1.26 gives 4.5 × 106 Pa)
(allow C.E. for values of T and area)
Page 46 of 64
(iii)
breaking stress is 65 × stress
copper is ductile
copper wire could extend much more before breaking
because of plastic deformation
extension to breaking point unlikely
any three (1)(1)(1)
7
[8]
30
(a)
(i)
0.4(0) m (1)
(ii)
speed ( = frequency × wavelength) = 22 × 0.4(0) ecf (1)
= 8.8 (m s–1) (1)
(ii)
90 or 450 (1) ° or degrees (1)
or 0.5π or 2.5π or 5π/2 (1) rad(ians)
or r or r (1) no R, Rad, etc
5
(b)
displacement of Y will be a positive (or ‘up’) maximum at 1/4
of a period (or cycle) (0.0114 s) (1)
returns to original position (at 0.5 of a period or cycle) (owtte) (1)
2
[7]
31
(a)
(i)
one ‘loop’ (accept single line only, accept single dashed line)
+ nodes at each bridge (± length of arrowhead)
+ antinode at centre (1)
1
(ii)
λ0 = 2L or λ = 0.64 × 2 (1)
= 1.3 (m) (1) (1.28)
2
(iii)
(c = f λ) = 108 × (a)(ii) (1)
= 138 to 140(.4) (m s–1) (1) ecf from (a) (ii)
2
Page 47 of 64
(b)
(i)
four antinodes (1) (single or double line)
first node on 0.16 m (within width of arrowhead)
+ middle node between the decimal point and the centre of the
‘m’ in ‘0.64 m’
+ middle 3 nodes labelled ‘N’, ‘n’ or ‘node’
(1)
2
(ii)
(4 f0 =) 430 (Hz) (1) (432)
or use of f =
gives 430 to 440 Hz
correct answer only, no ecf
1
(c)
decrease the length/increase tension/tighten string (1)
1
[9]
32
(a)
maximum displacement from equilibrium/mean
position/mid-point/etc (1)
1
(b)
(i)
any one from:
surface of water/water waves/in ripple tank (1)
rope (1)
slinky clearly qualified as transverse (1)
secondary (‘s’) waves (1)
max 1
(ii)
transverse wave: oscillation (of medium) is perpendicular to
wave travel
or transverse can be polarised
or all longitudinal require a medium (1)
1
Page 48 of 64
(c)
(i)
vertical line on B ± 5° (1)
1
(ii)
max 0, 180, 360 + min 90, 270 (1)
and line reaches same minimum and maximum every time
and reasonable shape (1)
2
Page 49 of 64
(d)
appropriate use (1)
reason for Polaroid filter being used (1)
eg
Polaroid glasses/sunglasses/
to reduce glare
windscreens
camera
reduce glare/enhance image
(in a) microscope
to identify minerals/rocks
polarimeter
to analyse chemicals/concentration
or type of sugar
stress analysis
reveals areas of high/low stress/
other relevant detail
LCD displays
very low power/other relevant
detail
3D glasses
enhance viewing experience, etc
2
[8]
33
(a)
the maximum displacement (of the wave or medium)
from the equilibrium position
accept ‘rest position’, ‘undisturbed position’, ‘mean position’
2
(b)
(vertically) downwards (¼ cycle to maximum negative displacement)
then upwards (¼ cycle to equilibrium position and ¼ cycle to maximum
positive displacement)
down (¼ cycle) to equilibrium position/zero displacement and correct
reference to either maximum positive or negative displacement or correct
reference to fractions of the cycle
candidate who correctly describes the motion of a knot 180 degrees out of
phase with the one shown can gain maximum two marks
(ie knot initially moving upwards)
3
Page 50 of 64
(c)
max 3 from
stationary wave formed
by superposition or interference (of two progressive waves)
knot is at a node
waves (always) cancel where the knot is
allow ‘standing wave’
3
[8]
34
(a)
(wave) B
(the parts of the) spring oscillate / move back and forth in direction of / parallel
to wave travel
OR
mention of compressions and rarefactions
Second mark can only be scored if first mark is scored
2
(b)
(i)
(double ended arrow / line / brackets) from between two points in phase
1
(ii)
wave A: arrow vertically upwards
wave B: arrow horizontally to the left
2
(c)
(transmitted radio waves are often) polarised
aerial (rods) must be aligned in the same plane (of polarisation / electric field) of
the wave
2
[7]
35
(a)
(i)
oscillates / vibrates
(allow goes up and down / side to side / etc, repeatedly, continuously, etc)
about equilibrium position / perpendicularly to central line
2
(ii)
X and Y: antiphase / 180 (degrees out of phase) / п (radians out of phase)
X and Z: in phase / zero (degrees) / 2п (radians)
2
Page 51 of 64
(b)
(i)
v = fλ
= 780 x 0.32 / 2 or 780 x 0.16 OR 780 x 320 / 2 or 780 x 160
THIS IS AN INDEPENDENT MARK
= 124.8
(m s–1) correct 4 sig fig answer must be seen
2
(ii)
¼ cycle
T = 1 / 780 OR = 1.28 × 10–3
0.25 × 1.28 × 10–3
= 3.2 × 10–4 (s)
Allow correct alternative approach using distance of 0.04m
travelled by progressive wave in ¼ cycle divided by speed.
0.04 /125
= 3.2 × 10–4 (s)
3
(c)
(i)
antinode
1
(ii)
2 x 0.240
= 0.48 m
‘480m’ gets 1 mark out of 2
2
(iii)
(f = v/λ = 124.8 or 125 / 0.48 ) = 260 (Hz) ecf from cii
1
[13]
36
(a)
(i)
π / 2 (radians) or 90 (degrees)
No path differences
Penalise contradictions
No fractions of a cycle
1
(ii)
3π / 2 (rad) or 270 (degrees)
No path differences
Penalise contradictions
No fractions of a cycle
1
Page 52 of 64
(b)
(oscillation or motion) perpendicular to direction of wave (travel / velocity / energy
transfer)
(oscillates from equilibrium to maximum positive displacement, back to equilibrium,
then to max negative displacement) and back to equilibrium / starting position / rest
position
do not allow ‘up and down’ for first mark
allow ‘up and down’, or ‘down then up’, ‘side to side’, ‘rise and fall’
in place of oscillates
Allow ‘rest position’, ‘starting position’ ,‘middle’, ‘centre line’
ref to nodes / antinodes not allowed for 2 nd mark
2
(c)
(the wave is) transverse OR not longitudinal
accept it is an S wave or secondary wave
only transverse can be polarised OR longitudinal waves cannot be polarised
OR oscillations are in one plane
2
(d)
(i)
number of waves / complete cycles / wavelengths (passing a point / produced)
per second
or ‘unit time’
allow: (number of) oscillations / vibrations / cycles per second
allow f=1 / T only if T is correctly defined
do not allow references to f=c / λ
1
(ii)
( v = f / λ λ = v / f = ) 4.5 × 103 / 6.0
= 750 (m)
correct answer only gets 2 marks
2
[9]
37
(a)
number of (complete) waves (passing a point) in 1 second
OR
number of waves / time (for the waves to pass a point)
OR
(complete number of) oscillations \ vibrations per second
OR
1 / T with T defined as time for 1 (complete) oscillation ✓
Allow: cycles
Allow: unit time
1
Page 53 of 64
(b)
For two marks:
oscillation of particles \ medium \ material etc, but not oscillation of wave is parallel to
\ in same direction as
the direction wave (travels) ✓ ✓
For one mark:
particles \ material \ medium move(s) \ disturbance \ displacement
parallel to \ in same direction as
the direction wave travels
OR
(oscillations) parallel to direction of wave travel ✓
the one mark answer with:
mention of compressions and rarefactions
OR
(longitudinal waves) cannot be polarised
gets two marks
✓
Allow
Vibration
Allow direction of energy transfer \ wave propagation
2
(c)
( f = 1540 / 0.50 × 10−3 )
= 3 100 000 (Hz) ✓ (3 080 000)
2sf ✓
2
(d)
no more than two points from either list (max 3):
Description
• mention of nodes and antinodes
• particles not moving at a node
• maximum displacement at antinode
• particles either side of node in antiphase / between two nodes in phase
• variation of amplitude between nodes
Explanation
• a stationary wave (forms)
• two waves are of equal frequency or wavelength (and amplitude in the same
medium)
• reflected and transmitted waves \ waves travelling in opposite directions, pass
through each other
• superpose / interference occurs
• constructive interference at antinodes
• destructive interference at nodes
✓✓✓
Allow ‘standing wave’
3
[8]
Page 54 of 64
38
39
40
C
[1]
C
[1]
(a)
Suitable experiment eg diffraction through a door / out of a pipe ✓
1
(b)
Using c = d / t
t = 2 500 / 480 = 5.2 s ✓
1
(c)
(Measured time is difference between time taken by light and time taken by sound)
Calculation assumes that light takes no time to reach observer, ie speed is infinite ✓
Do not allow “could not know speed of light”
1
(d)
Sound from gun is a mixture of frequencies. ✓
Alternative for 1st mark ‘(so speed is independent of frequency) the
sound of the gun is similar when close and far away’
1
All the sound reaches observer at the same time, ✓
1
(e)
More accurate, as it is closer to the accepted value. ✓
1
(f)
When θ = 0 °C
c = 331.29 m s–1
1
Therefore
331.29 = k √273.15 ✓
k = 20.045 ✓
1
(g)
The method and value are published ✓
1
other scientists repeat the experiment using the same method ✓
1
[10]
Page 55 of 64
Examiner reports
2
(a)
Many candidates incorrectly gave laser or sodium vapour lamp as a source producing a
continuous spectrum.
(b)
(i)
Many candidates correctly calculated the first angle.
(ii)
Many simply doubled the answer to part (i) to calculate the angular dispersion. Use of
the sine or tangent was relatively uncommon and even with error carried forward few
candidates gained the mark for the width of the first order spectrum.
(c)
5
6
7
8
Most candidates recognised that the intensity would fall because the energy was being
spread out over a larger area, many candidates recognised that this was an inverse square
relationship but only the strongest calculated the correct factor.
There were many highly competent and successful solutions to this simple question. However,
there were many significant figure and unit penalties – all the more surprising since the unit of the
answer was mentioned in the question itself.
(a)
A simple opening question that was well done by many apart from an extremely common
significant penalty deduction. Weaker candidates often did not recall that the sound pulse
travels to the wall and back again, thus travelling twice the 18m distance quoted in the
question.
(b)
This was not well done. Although a substantial number gained 2 out of 3 on a generous
mark scheme, only rarely did an answer give any sense that the pattern of maxima and
minima was fixed in space. Answers dealt exclusively with the cancellation issues with no
real discussion of the permanence of the cancellation of time and space.
Drawings were again very poor. Examiners awarded marks not only for correct directions of the
wavefronts but also for an awareness that wavefront spacings change in refraction and remain
unchanged in reflection. Candidates really must take more trouble over these relatively simple
drawings if they are not to throw away marks.
(a)
(i)
This was usually completed successfully. A significant proportion gave the answer as
2 s/10–5 m suggesting that they did not understand how axes are labelled.
(ii)
This was often correct but many incurred a significant figure penalty in this part. A
common error was to ignore the 10–4 on the d axis.
Page 56 of 64
(b)
(i)
The majority gave at least one correct reason and many were able to give two.
When discussing the fact that energy was absorbed many did not say where this was
occurring. Some suggested that energy was used up to transmit the wave through
the medium. Some responses seemed to be trying to express the spreading of the
energy of the wave and wrote unconvincingly about refraction and diffraction giving
insufficient detail.
(ii)
9
10
11
There were many correct answers but failure to realise that the pulse has to travel to
and from the reflecting object and incorrect powers of 10 lost many candidates a
mark.
(a)
Many were able to suggest that the wave in the rod is longitudinal.
(b)
Too many used the terms ‘echo’ or ‘refraction’ or ‘standing wave’ in their answers and
scored zero on this part.
(c)
Many candidates failed to recognise that the pulse travels to the end of the rod and back
again and thus lost marks by arriving at an answer that was half that required. Even those
who negotiated this hurdle frequently scored a significant penalty error.
Although almost all candidates recognised the need to square the Sun–Moon distance, some
could go no further and produced muddled and incorrect solutions.
Candidates who wrote the relevant formula down clearly and kept their work tidy were usually
able to arrive at a convincing and correct answer.
In part (a) diagrams and explanations varied from excellent to non-existent. The best candidates
provided a well-labelled diagram of an oscillating source radiating a longitudinal wave in air. They
went on to write about the vibrations of the source being passed on to the air molecules around
it, and the energy being propagated as the result of collisions between oscillating molecules.
Part (b) was quite often answered well, but some candidates confused polarisation with
diffraction and referred to a polarising slit for visible light.
Page 57 of 64
12
(a)
Although many appeared to know how to proceed the presentation of the argument was
usually very poor and examiners were frequently left to decipher a random array of figures
to ascertain whether this really was the case. The majority thought that taking two points on
the graph was adequate to demonstrate the law. Candidates should know that for two
points a straight line or any other curve could be drawn so that at least one extra set of
points needs to be considered to make a confident assertion that the particular curve
illustrates an inverse square law.
(b)
There were many correct answers but a common error was a misquote of the formula as
. A significant number of weaker candidates used
13
14
(a)
Very few did not know the type of wave although the spelling of longitudinal was often very
poor.
(b)
This was done very poorly with the majority incorrectly showing displacements of both
particles to the right
(c)
Most were able to gain at least one mark here and many gained both. Lack of clarity in the
response was often the cause of loss of the second mark.
(a)
(i)
Only about one-third of candidates were able to make a simple reading from the
graph in order to determine the wavelength of the wave.
(ii)
Many were able to operate with the equation c = fλ but a large number could not and
came to all sorts of grief. Too many used the value for the speed of an
electromagnetic wave, ignoring the value stated in the question.
(b)
16
17
.
The question asked for an interpretation of an ultrasound echo experiment and enabled
about half of candidates to score full marks. There were cases where candidates did not
remember that an echo requires the sound wave to go to the reflector and back again (a
factor of 2), but some were unable to interpret the graph and settled on inappropriate
values for the return time, both through misreads and through misinterpretation of what was
going on.
It was evident that the depth of knowledge necessary to answer this question was not available
to the majority of candidates. Even the energy transfer section in part (c) was the source of
wrong or vague or inadequate answers.
In part (a) many candidates struggled with their explanations and often contradicted themselves.
Although the question clearly specified a sound wave many candidates attempted explanations
in terms of a transverse wave and they could not transfer their understanding of wavelength to a
longitudinal wave. The rest position of particles was frequently mentioned. Explanations of
wavelength showed that the idea of phase is not understood well.
Page 58 of 64
Part (b) gave even the weakest candidates the opportunity to score full marks. λ was almost
always correct, but there were some candidates who made the usual mistakes of 2a. T / 2 and π
/ 2.
20
It was pleasing to see that a large number of candidates analysed the oscilloscope trace
correctly in part (a) and obtained the correct value for the time elapsing between the initial pulse
and the reflected pulse. There were some errors, as expected, in taking the reading from the
trace, some candidates for example, taking the start of the second pulse as the relevant point,
thus giving a total time of 8.0 ms. A significant number of candidates did not realise that the pulse
travelled back to the microphone, i.e. a total distance of 3 m.. This calculation again incurred
many significant figure penalties.
The answers to part (b) were, in general, slightly disappointing. The main problem was due to
candidates not reading the question properly and consequently not describing how the source
was connected to the oscilloscope (or Y plates). Many candidates did not describe how the
oscilloscope was set up, i.e. adjusting the voltage sensitivity and time base to give a trace, but
assumed that this had already been done. Some very neat traces were drawn but others were
sketched very casually and did not gain the allocated mark. The majority of candidates described
correctly how the period of the wave and hence the frequency was obtained from the trace.
24
29
This question was answered correctly by 58% of the candidates. Lack of understanding of radian
measure when considering phase difference probably accounted for 27% of the candidates
choosing distractor D (3π/2), rather than π/2.
Most candidates gave a correct frequency calculation in part (a), although unfortunately some
made a significant figure error in their final answer.
In part (b) (i), many candidates correctly calculated the angle between cable P and the ground or
the mast. Many were then able to calculate the tension correctly, although some lost the final
mark because they mistakenly doubled their answer, presumably on the grounds that the copper
wire pulled on each mast. In part (ii), most candidates knew the correct expression for the stress
but a significant number of candidates lost a mark through making an arithmetical error in the
calculation of the cross-sectional area of the wire, or lost the final two marks as a result of using
the expression for the surface area of the wire instead of the cross-sectional area. Other
candidates lost the final mark as a result of a unit error in the final answer or an arithmetical error
in the final calculation.
Many candidates scored two marks in part (iii) by comparing the breaking stress with their own
calculated value and reaching a valid conclusion. Some candidates gained these marks by
calculating the breaking force and comparing that with the tension in the wire. Very few
candidates considered other relevant points such as the ductile nature of copper.
Page 59 of 64
30
Most picked up full marks to parts (a) (i) and (ii).
Candidates tended to successfully state the phase difference and the unit to part (iii). A few
confused path difference with phase difference and gave an answer as a number of wavelengths.
Part (b) should have been a fairly easy question, but was quite poorly answered by many
candidates. There was much confusion over the meaning of displacement. Many thought point Y
goes down then up. Few stated that a positive peak is reached after ¼ period. Many referred to
wavelength rather than period or think that this is a stationary wave and the ‘node’ would not
move. Many believed point Y would move horizontally.
31
In part (a) (i), about 60% of candidates drew one ‘loop’ and picked up the mark. However, we
were fairly lenient on the shape of the ‘loop’ and students need to practice drawing these shapes.
Part (a) (ii) was expected to be a little easier than it was. 42% scored no marks on this despite
the benefit of an error carried forward from an incorrect part (a) (i). Many did not realise the
wavelength was found from the length of the string and knowledge of the shape of the
fundamental. Some candidates used λ = v/f with v = speed of light. In contrast, most candidates
found part (a) (iii) a very easy calculation.
The majority of candidates got four antinodes in part (b) (i), but then nearly half of those lost the
second mark by either not sketching the curve carefully enough or, more commonly, forgetting to
label the antinodes.
In part (c), the vast majority correctly suggested tightening or shortening the string. A few thought
that plucking harder would increase the pitch and some suggested increasing the length, using a
thinner string, increasing the wave speed, or even ‘play faster’.
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In part (a), the strict definition of amplitude was expected. Candidates needed to say ‘maximum
displacement’ and then indicate in some way that this was relative to the equilibrium position.
The majority, however, chose to define amplitude as the distance between the centre and the
peak.
For part (b) (i), the majority of candidates could not give an example of a transverse wave other
than electromagnetic waves. Most gave a form of electromagnetic radiation (most commonly
‘light’) or even sound. Common answers that were accepted included ‘water waves’, ‘waves on
strings’ or ‘s-waves’.
Most candidates realised that a comparison between the direction of wave travel and the
oscillation of the medium was a good way to answer part (b) (ii). It was common, however, for
candidates to struggle to express this clearly. The most common error was to say that a
transverse wave ‘moves’ perpendicular to the direction of wave travel rather than ‘oscillation is
perpendicular to direction of wave travel’.
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The vast majority of candidates found part (c) (ii) very straight forward.
The majority of candidates had no problem with part (c) (ii). The exact shape of the line was not
important as long as the maximum and minimum intensities appeared in the right place.
There were many very good answers to part (d), such as ‘sunglasses/ski goggles reduce glare
from light reflected from water/snow’ and ‘a camera filter reduces unwanted reflections’. Common
inadequate responses included saying that polarising sunglasses ‘reduce light intensity’ because
the lenses are ‘darker’, or that polarising filters reduce UV.
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Many students had learned the correct definition in part (a) but some gave a description, for
example ‘the greatest height of the wave from the middle’. This did not gain marks.
Surprisingly in answer to part (b), many students referred to the equilibrium position as the ‘node’
and maximum amplitude as the ‘antinode’ on a progressive wave. Many use fractions of a cycle
to describe the position of the knot but some use angles or fractions of a wavelength which are
not appropriate. The biggest loss of marks occurred in the first mark where a large number
thought that the knot would be travelling upwards initially.
Part (c) was a fairly easy question with students only needing to state that the ‘knot is at a node
on a stationary wave which is caused by superposition’ to get three marks. Most students
managed to get two of the marking points. Many did not understand how a node is formed,
believing it is the sum of a peak and a trough only, or that the whole rope is stationary, or that the
rope is only stationary at a node when cancellation occurs between waves that are 180° out of
phase. The two waves that form a stationary wave are not always 180° out of phase in order to
cancel at the nodes. Nodes are where the wave always cancels but the phase difference
between the waves repeatedly varies from zero to 2π. Cancellation everywhere on the stationary
wave only occurs when the waves are in antiphase but cancellation always happens at the nodes
because the displacements of the waves are always equal and opposite at those points (or
displacements are both zero when in phase and in antiphase). This is a complex situation but
there are many simulations available on the internet that help to get these ideas across.
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Most did well in part (b)(i) and indicated a complete wavelength very precisely, though a
generous tolerance was allowed. A significant number thought the coils constituted the waveform
and gave the spacing between one or two coils as the wavelength and some chose the
compression or the rarefaction or the whole length of the spring. In part (b)(ii) many believed
point P would move downwards. This is a very common misconception and a similar question
has appeared in a past paper. The behaviour of point Q is more difficult to understand. The
particle changes direction when the centre of a rarefaction or compression reaches it. If the wave
is moving to the right, then as the compression gets closer to the particle, the particle will move
left towards the compression.
In (c) the majority of students surprisingly did not recognise that this was about polarisation.
Those who did point this out did not describe the aerial being aligned with the plane of
polarisation.
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Part (a)(i) was almost universally misinterpreted due to a similar question appearing on a
previous paper. Many students interpreted the question as ‘describe the motion over the next
cycle’. Those who did this often failed to point out that there was a continuing oscillation taking
place. Part (a)(ii) was very poorly answered which was a surprise. A common answer was ‘out of
phase’ for X and Y which is not equivalent to ‘antiphase’. Phase was often given in terms of
number of wavelengths, e.g. ½λ. There was little understanding of the difference between phase
difference along a progressive wave and a stationary wave. Many had measured the fraction of a
wavelength between the points and converted this into an angle as you would for a progressive
wave. It is suggested that phase difference along a stationary wave be demonstrated by referring
to the many simulations available.
Part (b)(i) presented few problems for students. In part (b)(ii) many students did 1/780 and
obtained the time for one complete cycle but did not recognise that they needed to divide by 4 to
get the time for ¼ of a cycle. A significant number thought that the time between maximum
displacement and reaching the equilibrium position was half a cycle. Some divided 780 by 4
which makes the answer 8 times greater than it should be.
For part (c)(i) most students got ‘antinode’ but a significant number put ‘node’/ ‘amplitude’/ ‘max
displacement’ / ‘stationary wave’ / ‘equilibrium’ / ‘maxima’. Part (c)(ii) presented few problems for
students. In part (c)(iii) quite a few students left this blank because they were unable to answer
the previous question. However, many of those who scored the mark did so by using an incorrect
answer to (c)(ii). Students should be encouraged not to give up; the final part of a question is not
necessarily the hardest.
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(a)
(i)
Some candidates thought this was a stationary wave and thus stated incorrect phase
differences. See (a)(ii).
(ii)
Phase difference is generally not well understood by candidates. Phase differences
were often wrongly given in fractions of a wavelength e.g. λ / 4 rather than angles,
e.g. 90°. Ninety degrees was often also given as π / 4 radians or π radians rather than
π / 2 radians. Two hundred and seventy degrees was often thought to be equivalent
to π rather than 3 / 2 π radians.
Many said ‘in phase’ or ‘out of phase’ rather than stating the phase difference.
Many marks were lost here due to contradictions, where candidates attempting to
embellish their answers only succeeded in talking themselves out of the mark. E.g.’
90° (π / 4)’ or ‘90° (antiphase) ’. Where a question says ‘state’ and there is one mark
available, the candidate should try to give just the answer that they are confident is
correct and not try to expand upon it.
(b)
A high proportion of candidates thought that point B was going to go ‘downwards’.
Candidates must be clearer when stating directions. It is always advisable to say ‘vertically
upwards’ or ‘move upwards perpendicularly to the equilibrium line’. When a description of a
complete cycle is required, marks will be lost if the whole cycle is not described including,
in this case, the return to the equilibrium position.
(c)
Many came up with interesting hypotheses such as, that the wave must have passed
through a ‘crack’ in the rock to become polarised. However, in a question like this we are
only expecting the candidate to apply the physics that they know. Here we were only
looking for the link between polarisation and transverse waves, and not an in depth
knowledge of seismology.
(d)
This was very well done. A few candidates defined time period (T) rather than frequency.
There was a tendency for some to say ‘number of waves that pass a point in a given time’
rather than per second. A rather odd response to this question that was seen quite often
was: ‘The frequency doesn’t change’ . Quite a few stated the equation f = c/λ but this is not
the accepted definition of frequency.
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(a)
The majority of candidates got this mark and only a small number missed out the very
important ‘per second’.
(b)
For 2 marks it was necessary to point out that the particles are oscillating rather than the
wave oscillating. For example, some candidates said something like, ‘ waves oscillate
parallel to direction of wave’, or ‘ the motion is in the direction of the wave’.
Confusion between progressive waves and stationary waves was often seen and some
candidates talked about ‘ energy not being transferred with the wave’.
Many candidates talk about ‘motion’ of particles rather than oscillation. Part (a) and part (b)
highlight the fact that simple descriptions and definitions need to be memorised.
(c)
The first part was done well apart from some candidates who did not convert from mm to
m. Many rounded to 3sf rather than 2. This was probably because they believed 0.50 mm
was three significant figures.
(d)
This type of question is asking the student to apply their knowledge in a context that may
be unfamiliar (assessment objective AO2 – see specification).
A simple explanation describing the formation of a stationary wave was therefore needed
here.
However, many students did not spot that the question was about stationary waves.
Candidates could mention how nodes and antinodes are formed by superposition, etc.
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