[1]
(a)
6.
14
Examiner
only
Arholwr
yn unig
Figures A and B show two graphs which refer to the same wave.
displacement / mm
5·0
0
1·0
2·0
3·0
4·0
5·0
6·0
25·0
30·0
distance / m
–5·0
Fig. A
displacement / mm
5·0
0
5·0
10·0
15·0
20·0
Time / ms
–5·0
Fig. B
(i)
Deduce from the graphs
(I)
the amplitude of the wave,
[1]
......................................................................................................................................................................................................
(II)
the wavelength of the wave,
[1]
......................................................................................................................................................................................................
(III)
the period of the wave.
[1]
......................................................................................................................................................................................................
(0032/1)
15
(ii)
Examiner
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Hence find
(I)
the frequency of the wave,
[2]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(II)
the speed of the wave.
[2]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(iii)
(b)
The period and amplitude of the wave are kept constant, however its speed is
doubled. Sketch a curve to represent this change on Fig A.
[2]
The diagram shows an experimental set up to investigate the phenomenon of beats.
loudspeakers
Signal
generator
Signal
generator
A
(i)
B
Explain what is meant by the term beats.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(0032/1)
Turn over.
16
(ii)
Initially, A is set to a frequency of 450 Hz and B is set at 400 Hz. The frequency of B
is gradually and steadily increased to 500 Hz. Both signal generators are set to give
the same amplitude. Carefully explain what a stationary observer standing in front of
the two speakers would hear. Use numerical values to help clarify your answer.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
B is now switched off and A ( f = 450 Hz) is then sounded together with a tuning fork
of unknown frequency. A beat frequency of 3 Hz is heard. Calculate two possible
values for the frequency of the tuning fork.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iv)
Carefully explain how it would be possible to determine the correct value of the
tuning fork’s frequency using this experimental set up.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(0032/1)
Examiner
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[2]
3.
8
(a)
Complete the table below summarizing some of the key differences between progressive and
stationary (standing) waves.
[2]
Wave property
Stationary waves
Progressive waves
Zero at the nodes to
maximum at the antinodes.
Amplitude
Distance between two
consecutive particles
oscillating in phase.
Wavelength
(b)
Examiner
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Stationary waves in air can be demonstrated using a transparent closed resonance tube
containing a layer of fine dust. At the open end a loudspeaker connected to a signal
generator produces sound waves which travel to the closed end of the tube, where they are
reflected and interfere with the incident waves. The frequency of the signal generator is
varied until, at certain frequencies, stationary waves are formed. These are revealed to an
observer when the dust collects at nodes in regularly spaced heaps as shown.
resonance tube
Signal
Generator
20.0cm
=3400Hz
speaker
fine dust
(i)
Explain why the dust collects at the nodes.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Dust heaps are seen to collect when sound of frequency 3400Hz is played into the end
of the tube. The separation between the first and fifth heap is found to be 20.0 cm.
Calculate
(I)
the wavelength of the sound waves,
[2]
.......................................................................................................................................................................................
.......................................................................................................................................................................................
(II)
the speed of sound in air.
[2]
.......................................................................................................................................................................................
.......................................................................................................................................................................................
(c)
Explain why it is not good experimental practice to calculate the wavelength by measuring
the distance between adjacent heaps.
[2]
.......................................................................................................................................................................................
(0032/26)
[3]
9
(a)
4.
Sound is an example of a longitudinal wave. Explain what is meant by this statement.
[1]
Examiner
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Arholwr
yn unig
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(b)
(i)
The intensity of a wave has units of watts per metre2. Use this information to define
intensity.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
A small loudspeaker emits sound energy uniformly in all directions with a power of
5.0 watts. Calculate the intensity of the sound wave at a distance of 0.5 m from the
[2]
loudspeaker. [Area of spherical wave-front = 4 r2.]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(c)
Part of a graph of particle displacement vs. distance from speaker (at a certain time) is
shown below.
1.5
Displacement of molecules
from mean/10–9m
1.0
0.5
0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
-0.5
-1.0
-1.5
Distance from source/m
Find the amplitude 0.5m from the loudspeaker.
[1]
....................................................................................................................................................................................................................
(0032/26)
Turn over.
10
(d)
Examiner
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The intensity (I) is related to the amplitude (A) according to the following equation
Intensity = k ✕ (Amplitude)2
where k is a constant.
(i)
Use your answers to (b)(ii) and (c) to find the value of k.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
At a further distance from the source, the amplitude is found to be reduced by a factor
of 10 (i.e. it is 10 times less than the value calculated in (c)). Use your value of k to
calculate the intensity at this distance.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
By comparing your answers to (b)(ii) and (d)(ii) calculate the ratio of intensities.
[1]
....................................................................................................................................................................................................................
(0032/26)
[4]
4.
8
(a)
Examiner
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The speed, v of transverse waves along a stretched string having tension T, length l, and
mass m, is given by
T l
v2 = m
Show that the equation is correct as far as units (or dimensions) are concerned.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(b)
The diagram shows a stationary wave in a string under tension.
0.18m
pulley
vibration
generator
mass of string = 3
–3
10 kg
3·0 N
(i)
How many complete wavelengths are shown in the above diagram?
[1]
....................................................................................................................................................................................................................
(ii)
Explain how stationary waves are produced in the above set up.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(0032/1)
9
(iii)
Examiner
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Use the information given in the diagram, and the equation given in (a) to calculate
the speed of the wave in the string.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iv)
The tension in the string is reduced by a factor 4 (i.e. it is a quarter of the previous
value). By what factor will the speed v change?
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(0032/1)
Turn over.
[5]
7.
14
Examiner
only
Arholwr
yn unig
Water ripples are made to travel across the surface of a shallow tank by means of a vibrating
dipper. The dipper is set to oscillate up and down at a fixed frequency, f. At one instant the position
of the waves is shown in the cross-section below.
vibrating dipper
(a)
(i)
P
It is found that the waves travel a distance of 16·8 cm in 0·8 s.Calculate the speed of
the waves.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
State what is meant by the wavelength of a wave.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
The horizontal distance between a crest and a neighbouring trough is 1·5 cm.Calculate
the wavelength of the waves.
[1]
....................................................................................................................................................................................................................
(iv)
Calculate the frequency of the vibrating dipper.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(v)
Hence determine the period of the vibrating dipper.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(vi)
Draw, on the diagram, a double headed arrow to show the direction of the oscillating
motion of a particle at point P. Assume that the waves are transverse.
[1]
(vii)
Giving your answer in either degrees or fractions of a cycle, determine the phase
difference between the oscillations of points on the wave separated by 0·75 cm.
[1]
....................................................................................................................................................................................................................
(viii)
(0032/1)
Mark on the above diagram with the letter Q, one point which is 180° ( 1⁄2 of a cycle)
out of phase with point P.
[1]
15
(b)
Examiner
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The single dipper is now replaced by two identical dippers, S 1 and S2 as shown. They
oscillate in phase with the same frequency as the single dipper in (a). A stable interference
pattern is observed in the tank due to the superposition of the two waves generated by the
sources. The diagram shows the view from above and is actual size. R and T are two points
within the interference pattern.
S1
R
T
S2
(i)
State the Principle of Superposition.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Taking the necessary measurements and, clearly showing your reasoning, determine
whether R corresponds to a point of constructive interference or destructive
interference.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
Deduce the amplitude of the resulting wave at R.
[1]
....................................................................................................................................................................................................................
(iv)
T is a point, which is equidistant from S1 and S2. State the type of interference
expected here.
[1]
....................................................................................................................................................................................................................
(0032/1)
Turn over.
12
[6]
6.
(a)
Examiner
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An observer sees a farmer hammering in a fencepost. The time interval between each
hammer blow is 2·0 s. The observer, who is 660 m away, hears the blows coinciding with the
actual blows.
(i)
Explain why it is possible for this to occur.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Calculate a value for the speed of sound in air.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
Explain what the observer would see and hear if he walked towards the farmer.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iv)
Is there any other distance (closer or further away) between farmer and observer
where the observer would see and hear the blows again coinciding with each other?
Explain your answer.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(b)
A stationary wave is set up in a string. A student uses a flashing light to investigate the
shape of the string at various intervals. The student varies the frequency of the flashing light
until she notices the string alternate between its extreme positions as shown in the
following two diagrams.
DIAGRAM A
P
DIAGRAM B
(0032/26)
13
(i)
Examiner
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The flashes were 0·1s apart. Calculate two possible values for the period of the
stationary wave. Explain how you arrive at your answers.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Using one of your values for period, calculate a possible value for the frequency of
vibration of the string.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
Some positions along the string's length are permanently at rest.
(I)
What are these positions called?
[1]
......................................................................................................................................................................................................
(II)
(iv)
Label clearly on diagram A the position of one point where the string is
permanently at rest.
[1]
The length of the string is 2·0 m. Use this information and your answer to (b)(ii) to
calculate a possible value for the speed of transverse waves along the string.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(c)
(0032/26)
P is a point on the string. On diagram B,
(i)
label with the letter Q, one point which is in phase with P;
[1]
(ii)
label with the letter R, one point which is out of phase with P.
[1]
Turn over.
[7]
5.
2·0
10
Examiner
only
Arholwr
yn unig
In order to demonstrate beats, two loudspeakers connected to two separate signal generators
(sources A and B), of nearly equal frequencies and of the same amplitude, are sounded together.
The signals from the two generators are shown on the graphs.
displacement/arbitrary units
1·5
Source B
1
0·5
0
0·01
0·02
0·03
0·04
0·05
0·06
0·07
0·08
time/s
– 0·5
–1
Source A
–1·5
–2·0
(a)
(i)
Find, from the graphs
(I)
the period of source A,
[1]
......................................................................................................................................................................................................
(II)
the period of source B.
[1]
......................................................................................................................................................................................................
(ii)
Hence calculate the beat frequency.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(X032/1)
11
(b)
(i)
Examiner
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Estimate the resultant displacement at
(I)
time t = 0·0025 s,
[1]
......................................................................................................................................................................................................
(II)
time t = 0·0425 s.
[1]
......................................................................................................................................................................................................
(ii)
Describe briefly how the intensity of the sound varies between times t = 0·000s and
t = 0·085 s.
[1]
......................................................................................................................................................................................................
(c)
Describe and explain what would be heard if the period of source B were increased by
0·001s.
[2]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(X032/1)
Turn over.
6
[8]
2.
(a)
Examiner
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Distinguish between polarised and unpolarised light.
[2]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(b)
A light source appears at its brightest when viewed through two polaroid filters, A and B, as
shown in the diagram.
Light
Source
A
B
(i)
Describe carefully, by referring to the angle rotated, what is seen when polaroid B is
rotated slowly in its own plane through 180°.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Describe how you would use one of the polaroid filters to determine whether the light
from the source is polarised or not.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
7
(c)
(i)
Examiner
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The table shows three types of wave. Place a tick (✓) or a cross (×) in the column
next to each wave type to indicate whether or not they can be polarised in air.
[2]
Can be polarised (✓)
Wave type
Cannot be polarised (×)
Microwaves
Ultrasound
X-rays
(ii)
Give a reason for your answers to (c)(i).
[1]
....................................................................................................................................................................................................................
(541-01)
Turn over.
12
[9]
6.
(a)
Examiner
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List three properties of a progressive (sine) wave.
[3]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(b)
A displacement-distance graph (at a single instant in time) for a progressive wave in a string
is shown below. P is a particle of the string.
Displacement/
mm
20
15
10
5
0
0
20
P
40
60
80
–5
100
120
140
160
Distance/ mm
–10
–15
– 20
(i)
Determine
(I)
the amplitude of the wave,
[1]
......................................................................................................................................................................................................
(II)
the wavelength of the wave.
[1]
......................................................................................................................................................................................................
(ii)
The wave has a frequency of 3·0 Hz. Show that the distance travelled by the wave in
0·050 s is 12 mm.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
13
(iii)
(iv)
Examiner
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Assuming that the wave travels from left to right, draw on the graph the position of
the wave 0·050 s later.
[2]
(I)
(II)
Draw on the wave profile an arrow to show the direction of motion of particle
P at this time.
[1]
Estimate the displacement after 0·050 s of particle P.
[1]
......................................................................................................................................................................................................
(v)
Determine the phase difference (in degrees) between points on the wave that are
260 mm apart.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(c)
(i)
State the principle of superposition.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Diagrams A and B show two pulses approaching each other on a length of string. In
the spaces beneath, sketch a diagram in each case to illustrate the superposition of the
pulses as they cross.
[2] [1]
Diagram A
(541-01)
Diagram B
Turn over.
[10]
D
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[11]
7.
12
Examiner
only
Arholwr
yn unig
A loudspeaker connected to a signal generator is used to investigate sound.
Loudspeaker
(a)
(i)
Sound waves are described as being
progressive and longitudinal.
(I)
Explain what is meant by longitudinal
wave.
[1]
.............................................................................................
signal
generator
.............................................................................................
.............................................................................................
.............................................................................................
(II)
List two properties of a progressive wave.
[2]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(ii)
The signal generator is adjusted to give a frequency of 680 Hz. The sound wave
produced at a particular instant is represented by the following graph.
Displacement / 12
Arbitrary
Units
10
8
6
4
2
0
0·50
1·00
1·50
–2
–4
–6
–8
– 10
– 12
Distance from source / m
(541-01)
13
(I)
Examiner
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Suggest why the amplitude of vibration decreases with distance from the
speaker.
[1]
......................................................................................................................................................................................................
(II)
Use information from the graph to calculate the speed of sound.
[2]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(iii)
Write down the amplitude at 0·125 m and at 1·125 m from the speaker. Hence
calculate the ratio of the intensities at these distances.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(b)
The signal generator ( f = 680 Hz) and loudspeaker are now sounded together with a tuning
fork of unknown frequency. A beat frequency of 5 Hz is heard.
(i)
Use the beat frequency to calculate possible values for the frequency of the tuning
fork.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
It is noted that, as the frequency of the signal generator is increased, the beat
frequency also increases. Determine the actual value of the tuning fork’s frequency.
Explain your answer.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
Turn over.
14
(c)
Examiner
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The tuning fork is now removed and a large metal plate is placed at some distance from the
loudspeaker as shown in the diagram. A stationary wave is produced between the plate and
the loudspeaker.
Metal plate
Loudspeaker
signal
generator
(i)
What part does the metal plate play in producing the stationary wave?
[1]
....................................................................................................................................................................................................................
(ii)
List two properties of this type of wave.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(d)
Sound probe
Loudspeaker
signal
generator
Sound
meter
Metal
plate
A sound probe is moved slowly in a straight line from the loudspeaker to the plate, as
shown in the diagram. Explain carefully how a value for the speed of sound can be obtained
from this procedure.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
[12]
5.
(a)
7
Sound is a longitudinal wave. Explain the term longitudinal.
Examiner
only
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[1]
....................................................................................................................................................................................................................................
(b)
The speed of sound waves (v) in a metal rod can be given by the equation
v2 =
E
$
where E is the Young modulus of the metal and $ is the density of the metal.
(i)
Use the equation to find the speed of sound in a steel rod with Young modulus
2·1 ! 1011 Nm–2 and density 7800 kg m–3.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Show that the equation is correct in terms of units (or dimensions).
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
Two students stand a distance d apart beside a long steel rail on a still day. One
student places his ear against the rail while the other gives the rail a sharp knock with
a hammer. The first student hears two sounds, first the sound that travelled through
the steel rail and, 0·40s later, the sound that travelled through the air. Using your
answer to (b)(i), and given that the speed of sound in air is 330 ms –1, calculate d. [4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
Turn over.
[13]
7.
(a)
10
Examiner
only
Arholwr
yn unig
A Physics text book gives the following definition for stationary waves.
Stationary waves are oscillations that are formed when progressive waves of the same
amplitude and frequency, moving in opposite directions, superpose.
(i)
Explain the term amplitude.
[1]
....................................................................................................................................................................................................................
(ii)
Explain the term superpose.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(b)
A student sets up the following apparatus to investigate stationary waves on a string of
length 1·8 m.
string
vibration
generator
The student notices that, as the frequency of the vibration generator is steadily increased,
stationary waves are produced only at certain well-defined frequencies. The first stationary
wave to be seen (below) has one loop and occurs at a frequency of 12 Hz. P and Q are two
points on the string.
Q
P
f = 12 Hz
(541-01)
11
(i)
Examiner
only
Arholwr
yn unig
Compare the motion of points P and Q, paying attention to direction of motion,
amplitude and phase.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Show that the wavelength of this stationary wave is 3·6 m.
[1]
....................................................................................................................................................................................................................
(iii)
Calculate the speed of the waves travelling along the string.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(c)
(i)
The second stationary wave pattern seen has 2 loops and occurs at a frequency of
24 Hz. The third pattern has three loops and occurs at 36 Hz.
Sketch these patterns on the diagrams below.
[3]
f = 24 Hz
f = 36 Hz
(541-01)
Turn over.
12
(ii)
Examiner
only
Arholwr
yn unig
Complete the following table. Space is provided for your calculations.
Frequency / Hz
12
24
36
Number of loops
1
2
3
Wavelength /m
3·6
1
Wavelength
[5]
/m–1
Speed of waves / ms–1
1
Complete the graph of frequency against
. The frequency axis has been
Wavelength
inserted for you.
[1]
(iii)
Frequency / Hz
40
30
20
10
0
(iv)
1
Wavelength
Using your graph, state the relationship between frequency and wavelength.
/m–1
[1]
....................................................................................................................................................................................................................
(v)
Calculate the gradient of your graph. What does this gradient represent?
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
[14]
4.
7
Examiner
only
The following apparatus is set up to investigate stationary sound waves in air.
microphone
speaker
metal
plate
to signal
generator
(a)
Explain how stationary waves are produced in the space between the speaker and the metal
plate.
[3]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(b)
(i)
Calculate the separation between the nodes when the generator is set to 1700 Hz.
(Speed of sound in air = 340 ms–1 ).
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
The microphone initially detects no sound. It is then moved at a speed of 5 cms–1
towards the metal plate for 4 seconds. The intensity of the sound detected by the
microphone is recorded. Sketch, on the grid below, how the intensity varies over the
4 seconds. You are not expected to calculate values of intensity.
[3]
Intensity
(arbitrary units)
0
(iii)
1
2
3
What are the points of maximum intensity called?
4
Time (seconds)
[1]
....................................................................................................................................................................................................................
(541-01)
Turn over.
[15]
7.
(a)
12
Examiner
only
Figures A and B show two graphs which refer to the same transverse wave.
Figure A (Displacement at given time)
Displacement/cm
4
2
Distance/m
0
2
4
6
8
10
12
14
–2
–4
Figure B (Displacement at given distance from source)
Displacement/cm
4
2
0
Time/s
10
20
30
40
50
60
70
–2
–4
(i)
Mark clearly two points on figure A which are 2·5 wavelengths apart.
[1]
(ii)
Mark clearly two points on figure B which are 90° out of phase.
[1]
(iii)
Calculate the speed of the wave.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iv)
(541-01)
Draw another graph in figure A to represent a wave of the same frequency but double
the speed and half the amplitude.
[3]
13
(b)
Examiner
only
Two speakers are placed 1·25 m apart and are connected to the same signal generator so that
they act as coherent sources. A microphone is moved perpendicular to the speakers and in
the direction shown by the arrow. As it moves it detects a series of maxima and minima of
sound intensity. A maximum occurs at A, and the first minimum at B.
B
microphone
1·25 m
A
4·60 m
(i)
State what the microphone detects when it is moved, in the direction of the arrow,
beyond B.
[1]
....................................................................................................................................................................................................................
(ii)
Explain what is meant by coherent.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iii)
The Young double slit formula may be applied to this set-up. Calculate the
wavelength of the sound from the sources.
[4]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
Turn over.
14
(c)
Examiner
only
A listener stands outside a concert hall.
Sound proof walls
9m
20 m
Orchestra
9m
Listener
(i)
She notices that she can hear the orchestra through an open doorway, even though she
cannot see the orchestra. Explain how this is possible.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
She also notices that she can hear the low frequency notes better than the higher
notes. Explain why she is able to hear the low notes better. Use the concert hall
dimensions to support your answer. Take the speed of sound in the air to be 340 ms–1.
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
[16]
1.
(a)
3
Examiner
only
The clarinet is a ‘reed’ instrument. A reed is a thin strip of material which vibrates to
produce a sound. A musician, playing the clarinet in an orchestra, produces a note of
frequency 440 Hz. Calculate how many vibrations the reed will make before the sound
reaches a listener sitting 30 m away in the audience. Take the speed of sound to be 330 ms–1.
[3]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(b)
A second clarinet is now played together with the original. The second clarinet is slightly
out of tune with the original which results in a series of beats which the listener estimates to
have a frequency of 3 Hz.
(i)
What is meant by beats? Explain why beats arise in this situation.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
What is the beat period?
[1]
....................................................................................................................................................................................................................
(iii)
Write down two possible values for the frequency of the note produced by the second
clarinet.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(iv)
The frequency of the first clarinet is now increased to 445 Hz. The listener now
determines that the beat frequency has decreased. Showing clearly how you obtained
your answer, determine the frequency of the note played by the second clarinet. [2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(541-01)
Turn over.
[17]
(a)
5.
8
Examiner
only
State the principle of superposition.
[2]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(b)
The diagram shows an experimental set-up to measure the speed of sound in air. The double
beam oscilloscope displays the output from each microphone. When both microphones are
equidistant from the loudspeaker, which is emitting sound of frequency 850 Hz, the trace
on the oscilloscope is adjusted to appear as in the diagram.
Trace from
microphone 1
loudspeaker
Microphone 1
Microphone 2
Trace from
microphone 2
To signal generator
set to produce a
frequency of 850 Hz
Microphone 1 is kept stationary and microphone 2 is moved 0·2 m further away from the
loudspeaker in the direction of the arrow until the following trace is observed on the screen.
(541-01)
9
(i)
Examiner
only
Explain why the amplitude of the sound detected by microphone 2 has now
decreased.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Determine the phase difference between the sound now arriving at microphone 1 and
microphone 2.
[1]
....................................................................................................................................................................................................................
(iii)
Calculate the wavelength of the sound emitted by the loudspeaker.
[1]
....................................................................................................................................................................................................................
(iv)
Calculate a value for the speed of sound.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(c)
(541-01)
Microphone 1 is now moved 0·4 m towards the loudspeaker. Sketch carefully, on the
diagram below, the trace that might be expected from microphone 1. The trace from
microphone 2 has not changed and is shown.
[3]
Turn over.
[18]
6.
(a)
10
(i)
Examiner
only
A stretched string can carry both progressive and stationary waves. State how the
amplitude varies with position along the string for each of these waves.
Progressive wave:
......................................................................................................................................................................................................
......................................................................................................................................................................................................
Stationary wave:
......................................................................................................................................................................................................
......................................................................................................................................................................................................
[2]
(ii)
Explain how the energy flow for a progressive wave differs from that for a stationary
wave.
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
[2]
(b)
Two points (P and Q) on a progressive wave differ in phase by 90 °. The distance between
them is 0·30 m and their period of oscillation is 0·050 s. P is shown on the following sketch.
P
(i)
Label a possible position for Q on the above sketch.
(ii)
Define wavelength, and calculate its value for this wave.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
[3]
(541-01)
11
(iii)
Examiner
only
Calculate the speed of the wave.
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
[3]
(iv)
The amplitude of the wave is 0·020 m. Calculate the mean speed of particle P over
one complete cycle.
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
[2]
(c)
The following apparatus is set up to study stationary waves in a string of length 1·8 m. The
vibration generator is set to 10·4 Hz initially in order to produce a stationary wave with three
‘loops’ as shown.
1·8 m
vibration
generator
(i)
Label a node on the above sketch.
[1]
(ii)
Show on the diagram three points R, S and T that oscillate in phase.
[1]
(iii)
Calculate the speed of the wave.
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
[2]
(iv)
When the frequency of the vibration generator is doubled, the number of loops
observed increases to six. Explain carefully how this change would affect, if at all, the
speed of the wave.
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
[3]
(541-01)
Turn over.
[19]
1.
3
Examiner
only
A progressive wave is travelling from left to right. Displacement – time graphs are given for the
same time interval for two points, A and B, in the path of the wave. B is 0·30 m to the right of A.
displacement at B / m
displacement at A / m
0·05
0·05
t/s
0
0·1
0·2
0·3
0·4
– 0·05
(a)
0
t/s
0·1
0·2
0·3
0·4
– 0·05
(i)
Write down the value of the amplitude of the wave.
(ii)
Calculate the frequency.
........................................................
[1]
[3]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(b)
Show that 6·0 m s–1 is a possible speed for the waves, explaining your reasoning carefully.
[2]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(c)
(i)
Explain what is meant by the wavelength of the waves.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
Taking the wave speed as 6·0 m s–1, calculate the wavelength of the waves.
[1]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
542-01
Turn over.
[20]
2.
(a)
4
Examiner
only
In the set-up below, a microwave sensor is moved slowly in a straight line at right angles to
the central axis. Successive maxima of microwave intensity are found at the points marked
by crosses.
microwave
S1
source
metal plate
with parallel
slits S1 and S2
VIEW FROM ABOVE
(NOT TO SCALE)
+
0·096 m
+
central axis
+
S2
+
0·075 m
0·60 m
+P
microwave
sensor
(i)
Explain what part diffraction plays in the formation of this pattern.
[2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(ii)
The slits S1 and S2 act as in-phase sources.
(I)
Explain what is meant by in-phase sources.
[1]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(II)
State one feature of the diagram which confirms that S1 and S2 are in-phase. [1]
......................................................................................................................................................................................................
(iii)
Assuming that the Young’s double slits formula is applicable, use the data in the
diagram to show that the wavelength of the microwaves is approximately 0·01 m. [2]
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
....................................................................................................................................................................................................................
(542-01)
5
(iv)
(I)
Examiner
only
What can be said about the phase of the waves from S1 and S2 when they arrive
at point P? Justify your answer.
[2]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(II)
Calculate the path difference, S1P – S2P, explaining your reasoning.
[3]
......................................................................................................................................................................................................
......................................................................................................................................................................................................
......................................................................................................................................................................................................
......................................................................................................................................................................................................
(b)
The microwave source of part (a) emits polarised waves. Describe how you would
demonstrate this.
[2]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(c)
Potatoes can be heated quickly in a microwave oven. Which properties of the microwave
radiation account for this?
[2]
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
....................................................................................................................................................................................................................................
(542-01)
Turn over.
[21]
1.
2
Examiner
only
A piece of string 1.8 m long is attached at one end to the pin of a vibration generator and, at
the other end, to a rigid wall. The diagrams show the string at intervals of 0.0030 s, starting
from shortly after the generator has been connected to the signal generator (so the wave has
not yet reached the wall).
pin
wall
(a)
Calculate
(i)
the speed of the waves,
[2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(ii)
the frequency.
[3]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
1322-01)
3
(i)
Write down two distances from the generator at which there are nodes.
[1]
.........................................................................................................................................................................................................
(ii)
(I)
Describe how the amplitude of the stationary wave varies with distance
along the string.
[2]
............................................................................................................................................................................................
............................................................................................................................................................................................
............................................................................................................................................................................................
(II)
Explain whether or not the same description applies to the amplitude of the
progressive wave (see previous page).
[1]
............................................................................................................................................................................................
............................................................................................................................................................................................
............................................................................................................................................................................................
(c)
Explain in terms of interference how the stationary wave is formed and, in particular,
how nodes arise.
[3]
........................................................................................................................................................................................................................
........................................................................................................................................................................................................................
........................................................................................................................................................................................................................
........................................................................................................................................................................................................................
........................................................................................................................................................................................................................
Turn over.
03
Later on a stationary wave develops. Refer to the shaded area below.
1322 01
(b)
Examiner
only
[22]
2.
4
Examiner
only
Two loudspeakers are placed 2.0 m apart, and facing the same way, in the middle of a playing
field, on a calm day. They are connected to the same signal generator, and therefore produce
sound of the same frequency.
VIEW FROM ABOVE
(NOT TO SCALE)
(a)
A student walks slowly along the line AB, and hears the sound varying regularly in
loudness as he walks. The positions where the sound is loudest are 1.8 m apart.
(i)
Use the Young’s fringes formula to calculate the wavelength of the sound.
[2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(ii)
Suggest why the results would be less reliable if the experiment were performed in
a hall, that is surrounded by walls.
[1]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(b)
The student now stops at a point where the sound is quietest. The teacher then
disconnects one of the loudspeakers. The student now hears a louder sound. Explain
why the sound is louder. Your answer should mention phase.
[3]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(1322-01)
5
(c)
Examiner
only
The disconnected loudspeaker is reconnected, but with the wires to its terminals
swapped over, so that the loudspeakers are now sound sources in antiphase (exactly out
of phase). What difference will be observed by the student if he repeats the walk of
part (a)?
[1]
........................................................................................................................................................................................................................
........................................................................................................................................................................................................................
(d)
State, giving your reasoning, how the separation between points of quietest sound
along AB would change if
(i)
the separation of the loudspeakers were doubled (to 4.0 m),
[2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(ii)
the signal generator were adjusted so that the frequency of sound emitted by the
loudspeakers were doubled. [The loudspeaker separation is restored to 2.0 m] [2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(1322-01)
Turn over.
1322 01
05
.........................................................................................................................................................................................................
[23]
1.
(a)
2
(i)
Sound waves in air are longitudinal. Explain what this means.
Examiner
only
[2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(ii)
What is meant by the wavelength of a progressive sound wave?
[1]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
axis
roughly 2 m
(b)
In the set-up shown, both loudspeakers are connected to the same signal generator.
(i)
Explain briefly why a stationary wave is produced.
[2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
(ii)
With the signal generator set to 750 Hz, the quietest points on the axis are found
to be 0.22 m apart. Calculate a value for the speed of sound, giving your
reasoning.
[3]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
1322-01)
3
(iii)
Examiner
only
Show that it would not be possible to use this method, with the set-up just as
shown, if the signal generator were set to 50 Hz.
[2]
.........................................................................................................................................................................................................
.........................................................................................................................................................................................................
1322
010003
.........................................................................................................................................................................................................
1322-01)
Turn over.
[24]
1.
(a)
2
Examiner
only
A water wave is travelling from left to right along a canal. The diagram shows the wave
at one instant.
A
2.0 m
B
direction of travel of wave
(i)
(I)
(II)
(ii)
Show that the wavelength of the wave is 0.80 m.
[1]
How do the amplitudes compare for water particles A and B?
[1]
A graph of displacement, y (vertical
component) against time is given
alongside for water particle A.
(I)
Calculate the frequency. [1]
y/m
PARTICLE A
0.1
0
0
0.2
0.4
time / s
– 0.1
y/m
PARTICLE B
0.1
0
(II)
(iii)
Sketch the corresponding
graph for particle B on the
axes given.
[2]
Calculate the speed of the wave.
© WJEC CBAC Ltd.
(1322-01)
0
0.2
0.4
time / s
– 0.1
[1]
3
When the wave in the first diagram has travelled further, it reaches a length of the canal
where the water is shallower. The wavelength in the shallow water is 0.60 m.
Calculate the speed of the wave in the shallow water, giving your reasoning.
[2]
13 2 2
010 0 0 3
(b)
Examiner
only
© WJEC CBAC Ltd.
(1322-01)
Turn over.
[25]
3.
6
The cavity of a laser has reflecting ends a distance L apart. Assuming there is a node at each
end, the possible wavelengths of stationary waves are given by the equation
2L
Q = n
in which n is a whole number.
(a)
Label relevant lengths on the diagram, and hence show how this equation arises. [The
stationary wave is shown as if it were a stationary wave on a stretched string.]
[2]
(b)
For a particular semiconductor laser, L = 0.2050 mm.
(c)
(i)
Using the equation above, show that a stationary wave of wavelength 820.0 nm can
exist in the cavity, but that a stationary wave of wavelength 821.0 nm cannot. [2]
(ii)
Find the next wavelength above 820.0 nm of stationary wave that could exist in the
cavity.
[2]
A stationary wave is equivalent to a superposition of progressive waves of equal
amplitude travelling in opposite directions. Why is this condition not exactly met in a
laser emitting a beam of light?
[2]
© WJEC CBAC Ltd.
(1322-01)
Examiner
only