Download practice test on waves

1.
This question is about waves and wave properties. --The diagram below shows three wavefronts incident on a boundary between medium I and
medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete.
C
A
E
F
medium I
medium R
B
(a)
(i)
D
On the diagram above, draw a line to complete the wavefront EF.
(1)
(ii)
Explain in which medium, I or R, the wave has the higher speed.
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(3)
1
The graph below shows the variation with time t of the velocity v of one particle of the medium
through which the wave is travelling.
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6
4
v / ms–1
2
0
0
1
2
3
4
–2
5
6
7
t / ms
–4
–6
–8
(b)
(i)
Explain how it can be deduced from the graph that the particle is oscillating.
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(2)
(ii)
Determine the frequency of oscillation of the particle.
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(2)
(iii)
Mark on the graph with the letter M one time at which the particle is at maximum
displacement.
(1)
(iv)
Estimate the area between the curve and the x-axis from the time t = 0 to the time
t = 1.5 ms.
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(2)
(v)
Suggest what the area in b (iv) represents.
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(1)
2
(c)
(i)
State the principle of superposition.
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(2)
Two loudspeakers S1 and S2 are connected to the same output of a frequency generator and are
placed in a large room as shown below.
P
560 cm
580 cm
S1
M
550 cm
S2
Sound waves of wavelength 40 cm and amplitude A are emitted by both loudspeakers.
M is a point distance 550 cm from both S1 and S2. Point P is a distance 560 cm from S1 and 580 cm
from S2.
(ii)
State and explain what happens to the loudness of the sound detected by a
microphone when the microphone is moved from point M to point P.
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(4)
(iii)
Referring to the diagram above, the amplitude of the wave emitted by S1 is now
increased to 2A. The wave emitted by S2 is unchanged. Deduce what change, if any,
occurs in the loudness of the sound at point M and at point P when this change in
amplitude is made.
at point M: ......................................................................................................
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at point P:
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(4)
(iv)
The loudspeakers are now replaced with two monochromatic light sources. State the
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reason why bright and dark fringes are not observed along the line PM.
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(1)
Waves of frequency f and speed c are emitted by a stationary source of sound. An observer moves
along a straight line towards the source at a constant speed v.
(d)
State, in terms of f, c and v, an expression for
(i)
the wavelength of the sound detected by the observer.
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(1)
(ii)
the apparent speed of the wave as measured by the observer.
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(1)
The observer carries a second source of sound, producing waves of the same actual frequency and
speed as the stationary source. Whilst moving, the observer detects a beat frequency of 6.0 Hz for
sound waves emitted by the sources of frequency 500 Hz and speed 340 ms–1.
(e)
(i)
Describe what is meant by beats.
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(2)
(ii)
Calculate the speed v of the observer.
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(3)
(Total 30 marks)
2.
This question is about Huygens’ principle and refraction.
(a)
State Huygens’ principle.
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(1)
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Diagram 1 below shows a wave that approaches the boundary between medium 1 and medium 2.
AB and CD are two wavefronts of the wave.
Diagram 2 shows the situation a time later when point C of the wavefront CD has just reached the
boundary. The speed of the wave in medium 1 is v1 and the speed in medium 2 is v2. v1 is greater
than v2.
Diagram 1
Diagram 2
D
C
B
D
1
medium 1
medium 2
(b)
B
A
C
On diagram 2 above
(i)
draw the wavefront AB.
(1)
(ii)
draw a line to represent the distance travelled by point A.
(1)
(iii)
label the distance travelled by point B with the letter “s”.
(1)
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(c)
Use your completed diagram 2 to derive the relation
sin θ1
sin θ 2

v1
v2
where θ1 is the angle of incidence and θ2 is the angle of refraction.
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(d)
In medium 1 the wave has a wavelength of 4.0 cm and travels at a speed of 8.0 cm s–1.
Determine the frequency of the wave in medium 2.
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(2)
(e)
The angle of incidence is 60° and the angle of refraction is 35°. Calculate the speed of the
wave in medium 2.
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(2)
(Total 14 marks)
3.
This question is about wave properties and interference.
The diagram below represents the direction of oscillation of a disturbance that gives rise to a wave.
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(a)
By redrawing the diagram in the spaces below, add arrows to show the direction of wave
energy transfer to illustrate the difference between
(i)
a transverse wave and
(1)
(ii)
a longitudinal wave.
(1)
7
A wave travels along a stretched string. The diagram below shows the variation with distance
along the string of the displacement of the string at a particular instant in time. A small marker is
attached to the string at the point labelled M. The undisturbed position of the string is shown as a
dotted line.
Directions of wave travel
M
(b)
On the diagram above
(i)
draw an arrow to indicate the direction in which the marker is moving.
(1)
(ii)
indicate, with the letter A, the amplitude of the wave.
(1)
8
(iii)
indicate, with the letter λ, the wavelength of the wave.
(1)
(iv)
T
later, where T is the period of
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oscillation of the wave. Indicate, with the letter N, the new position of the marker.
draw the displacement of the string a time
(2)
The wavelength of the wave is 5.0 cm and its speed is 10 cm s–1.
(c)
Determine
(i)
the frequency of the wave.
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(1)
(ii)
how far the wave has moved in
T
s.
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Interference of waves
(d)
By reference to the principle of superposition, explain what is meant by constructive
interference.
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(4)
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The diagram below (not drawn to scale) shows an arrangement for observing the interference
pattern produced by the light from two narrow slits S1 and S2.
P
ya
S1
monochromatic
light source
d M
O
X
S2
D
single
slit
double slit
screen
The distance S1S2 is d, the distance between the double slit and screen is D and D
d such that
the angles θ and  shown on the diagram are small. M is the mid-point of S1S2 and it is observed
that there is a bright fringe at point P on the screen, a distance yn from point O on the screen. Light
from S2 travels a distance S2X further to point P than light from S1
(e)
(i)
State the condition in terms of the distance S2X and the wavelength of the light λ, for
there to be a bright fringe at P.
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(2)
(ii)
Deduce an expression for θ in terms of S2X and d.
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(2)
(iii)
Deduce an expression for  in terms of D and yn.
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(1)
10
For a particular arrangement, the separation of the slits is 1.40 mm and the distance from the slits
to the screen is 1.50 m. The distance yn is the distance of the eighth bright fringe from O and the
angle θ = 2.70 × 10–3 rad.
(f)
Using your answers to (e) to determine
(i)
the wavelength of the light.
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(2)
(ii)
the separation of the fringes on the screen.
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(3)
(Total 24 marks)
4.
This question is about waves and wave motion.
(a)
(i)
Define what is meant by the speed of a wave.
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(2)
(ii)
Light is emitted from a candle flame. Explain why, in this situation, it is correct to
refer to the “speed of the emitted light”, rather than its velocity.
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(2)
(b)
(i)
Define, by reference to wave motion, what is meant by displacement.
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(2)
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(ii)
By reference to displacement, describe the difference between a longitudinal wave
and a transverse wave.
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(3)
The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S
waves). The graph below shows the variation with time t of the distance d moved by the two types
of wave.
d / km
S wave
P wave
1200
800
400
0
0
(c)
25
50
75
100
125
150
175
200
225
t/s
Use the graph to determine the speed of
(i)
the P waves.
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(1)
(ii)
the S waves.
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(1)
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The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1, L2
and L3. The laboratories are at the corners of a triangle so that each is separated from the others by
a distance of 900 km, as shown in the diagram below.
900 km
L1
L2
L3
The records of the variation with time of the vibrations produced by the earthquake as detected at
the three laboratories are shown below. All three records were started at the same time.
L1
L2
start of trace
L3
time
On each record, one pulse is made by the S wave and the other by the P wave. The separation of
the two pulses is referred to as the S-P interval.
(d)
(i)
On the trace produced by laboratory L2, identify, by reference to your answers in (c),
the pulse due to the P wave (label the pulse P).
(1)
(ii)
Using evidence from the records of the earthquake, state which laboratory was
closest to the site of the earthquake.
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(1)
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(iii)
State three separate pieces of evidence for your statement in (d)(ii).
(3)
1.
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2.
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3.
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(iv)
The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively.
Use the graph, or otherwise, to determine the distance of the earthquake from each
laboratory. Explain your working.
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Distance from L1 = ......................km
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Distance from L2 = ......................km
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Distance from L3 = ......................km
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(4)
(v)
Mark on the diagram a possible site of the earthquake.
(1)
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There is a tall building near to the site of the earthquake, as illustrated below.
building
ground
direction of vibrations
The base of the building vibrates horizontally due to the earthquake.
(e)
(i)
On the diagram above, draw the fundamental mode of vibration of the building
caused by these vibrations.
(1)
The building is of height 280 m and the mean speed of waves in the structure of the building is
3.4 × 103 ms–1.
(ii)
Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to
be very destructive.
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(3)
(Total 25 marks)
5.
This question is about waves and wave motion.
(a)
Describe, by reference to the propagation of energy, what is meant by a transverse wave.
Transverse wave
(2)
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(b)
State one example, other than a wave on a string, of a transverse wave.
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(1)
A transverse wave is travelling along a string that is under tension. The diagram below shows the
displacement of part of the string at time t = 0. The dotted line shows the position of the string
when there is no wave travelling along it.
displacement / cm
5.0
(c)
15
25
35
distance along string / cm
45
On the diagram above, draw lines to identify for this wave
(i)
the amplitude (label this A).
(1)
(ii)
the wavelength (label this λ).
(1)
(d)
The period of the wave is 1.2 × 10–3 s. Deduce that the speed of the wave is 250 m s–1.
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(2)
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(e)
Using the axes below, draw the displacement of the string when t = 3.0 × 10–4 s. (The
displacement of the string at t = 0 is shown as a dotted line.)
displacement / cm
5.0
15
25
35
distance along string / cm
45
(3)
The string is maintained at the same tension and is adjusted in length to 45 cm. It is made to
resonate at its first harmonic (fundamental) frequency.
(f)
Explain what is meant by resonance.
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(2)
(g)
Describe how the string can be made to resonate at its first harmonic frequency only.
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(2)
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(h)
Determine the frequency of the first harmonic of the string.
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(2)
(Total 16 marks)
6.
This question is about sound waves.
In order to demonstrate two-source interference of sound waves, two loudspeakers are connected
to the same output of a signal generator. The loudspeakers are fixed 4.0 m apart.
In the diagram below, the line AB is parallel to the loudspeakers and at a distance of 10.0 m from
the loudspeakers. Point P is midway between the loudspeakers.
A
signal
generator
10.0 m
P (loud)
4.0 m
Q (quiet)
R (loud)
B
Katerina walks along the line AB carrying a microphone connected to a detector. She registers a
sound that alternates in intensity from loud to quiet.
(a)
Describe the conditions necessary for a sound of minimum intensity to be registered at Q.
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(3)
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As Katerina runs along the line AB she counts the number of loud sounds registered in a given
time. The frequency of the sound emitted by both loudspeakers is 360 Hz and the speed of sound
in air is 330 ms–1.
(b)
Estimate the speed at which she is running if the maximum sounds occur with a frequency
of about 2 Hz.
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(6)
One of the loudspeakers is now disconnected from the source and connected to another signal
generator as shown below.
A
signal
generator
frequency = f 1
10.0 m
P (loud)
4.0 m
signal
generator
frequency = f 2
B
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(c)
The frequencies of both generators are altered. With this new arrangement, Katerina now
stands at the point P and registers a sound of frequency 360 Hz that varies in amplitude at a
frequency of 2.0 Hz. Explain quantitatively how this observation arises.
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(3)
(Total 12 marks)
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