8.2 Waves-New

AS- PHYSICS-WORK-SHEET MD.
KAMRUZZAMAN
TOPIC-WAVES O/A LEVEL PHYSICS & MATHS TEACHER
Ph-01733455066
Name………………………………………………………………………date………………………………..……………………
S-15/V21/Q6
Q1 (a) State what is meant by diffraction and by interference.
diffraction: ..........................................................................................................................................................................
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interference: .......................................................................................................................................................................
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[3]
(b) Light from a source S1 is incident on a diffraction grating, as illustrated in Fig. 6.1.
Fig. 6.1 (not to scale)

The light has a single frequency of 7.06 × 1014 Hz. The diffraction grating has 650 lines per millimeter.
Calculate the number of orders of diffracted light produced by the grating. Do not include the zero order.
Show your working.
number = .......................................................... [3]
(c) A second source S2 is used in place of S1. The light from S2 has a single frequency lower than that of the light from
S1. State and explain whether more orders are seen with the light from S2.
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S-15/V22/Q6
Q2 (a) State two differences between progressive waves and stationary waves.
1. ......................................................................................................................................................................................
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2. ......................................................................................................................................................................................
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[2]
(b) A source S of microwaves is placed in front of a metal reflector R, as shown in Fig. 6.1.
Fig. 6.1
A microwave detector D is placed between R and S.
Describe
(i) how stationary waves are formed between R and S,
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(ii) how D is used to show that stationary waves are formed between R and S,
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(iii) how the wavelength of the microwaves may be determined using the apparatus in Fig. 6.1.
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(c) The wavelength of the microwaves in (b) is 2.8 cm. Calculate the frequency, in GHz, of the microwaves.
frequency = ................................................. GHz [3]

S-15/V23/Q6
Q3 (a) Two overlapping waves of the same type travel in the same direction. The variation with
distance x of the displacement y of each wave is shown in Fig. 6.1.
Fig. 6.1
The speed of the waves is 240 m s–1. The waves are coherent and produce an interference
pattern.
(i) Explain the meaning of coherence and interference.
coherence: .........................................................................................................................................................................
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interference: .......................................................................................................................................................................
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[2]
(ii) Use Fig. 6.1 to determine the frequency of the waves.
frequency = .................................................... Hz [2]
(iii) State the phase difference between the waves.
phase difference = ........................................................ ° [1]

(iv) Use the principle of superposition to sketch, on Fig. 6.1, the resultant wave. [2]
(b) An interference pattern is produced with the arrangement shown in Fig. 6.2.

Laser light of wavelength λ of 546 nm is incident on the slits S1 and S2. The slits are a distance 0.13 mm apart. The
distance between the slits and the screen is 85 cm. Two points on the screen are labelled A and B. The path difference
between S1A and S2A is zero. The path difference between S1B and S2B is 2.5 λ. Maxima and minima of intensity of
light are produced on the screen.
(i) Calculate the distance AB.
distance = ...................................................... m [3]
(ii) The laser is replaced by a laser emitting blue light. State and explain the change in the distance between the maxima
observed on the screen.
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W-15/V21/Q6
Q4 (a) A progressive wave transfers energy. A stationary wave does not transfer energy. State two other differences
between progressive waves and stationary waves.
1. ......................................................................................................................................................................................
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2. ......................................................................................................................................................................................
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[2]
(b) A stationary wave is formed on a stretched string between two fixed points A and B.
The variation of the displacement y of particles of the string with distance x along the string
for the wave at time t = 0 is shown on Fig. 5.1.
Fig. 5.1
The wave has a period of 20 ms and a wavelength of 1.2 m. The maximum amplitude of the particles
of the string is 5.0 mm.
(i) On Fig. 5.1, draw a line to represent the position of the string at t = 5.0 ms. [2]
(ii) State the phase difference between the particles of the string at x = 0.40 m and at x = 0.80 m.
phase difference = ......................... unit .................... [1]
(iii) State and explain the change in the kinetic energy of a particle at an antinode between t = 0 and t = 5.0 ms. A
numerical value is not required.
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W-15/V22/Q7
Q5 An arrangement that is used to demonstrate interference with waves on the surface of water is shown in Fig. 7.1.
Fig. 7.1 (view from above)

(a) Two dippers D1 and D2 are connected to a motor and a d.c. power supply. Initially only D1 vibrates on the water
surface to produce waves.
The variation with distance x from D1 of the displacement y of the water at one instant of time is shown in Fig. 7.2.
Fig. 7.2
Using Fig. 7.2, determine
(i) the amplitude of the wave,
amplitude = ................................................... mm [1]
(ii) the wavelength of the wave.
wavelength = ................................................... mm [1]
(b) The two dippers D1 and D2 are made to vibrate and waves are produced by both dippers on the water surface.
(i) State and explain whether these waves are stationary or progressive.
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(ii) Explain why D1 and D2 are connected to the same motor.
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(c) The points A and B on Fig. 7.1 are at the distances from D1 and D2 shown in Fig. 7.3.
Fig. 7.3
State and explain the variation with time of the displacement of the water on the surface at
(i) A,...................................................................................................................................................................................
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........................................................................................................................................................................................[2]
(ii) B....................................................................................................................................................................................
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W-15/V23/Q2
Q6 A signal generator is connected to two loudspeakers L1 and L2, as shown in Fig. 2.1.
Fig. 2.1
A microphone M, connected to the Y-plates of a cathode-ray oscilloscope (c.r.o.), detects the intensity of sound along the
line ABC.
The distances L1A and L2A are equal.
The time-base of the c.r.o. is switched off.
The traces on the c.r.o. when M is at A, then at B and then at C are shown on Fig. 2.2, Fig. 2.3 and Fig. 2.4 respectively.
Fig. 2.2 Fig. 2.3 Fig. 2.4

For these traces, 1.0 cm represents 5.0 mV on the vertical scale.
(a) (i) Explain why coherent waves are produced by the loudspeakers.
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(ii) Use the principle of superposition to explain the traces shown with M at
1. A,....................................................................................................................................................................................
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2. B,...................................................................................................................................................................................
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3. C......................................................................................................................................................................................
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(b) The sound emitted from L1 and L2 has frequency 500 Hz. The time-base on the c.r.o. is switched on.
The microphone M is placed at A.
On Fig. 2.5, draw the trace seen on the c.r.o.
On the vertical scale, 1.0 cm represents 5.0 mV. On the horizontal scale, 1.0 cm represents 0.10 ms.
Fig. 2.5 [3]

F-16/V22/Q4
Q7 (a) (i) By reference to the direction of propagation of energy, state what is meant by a transverse wave.
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(ii) State the principle of superposition.
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(b) Circular water waves may be produced by vibrating dippers at points P and Q, as illustrated inFig. 4.1.
The waves from P alone have the same amplitude at point R as the waves from Q alone. Distance PR is 44 cm and
distance QR is 29 cm. The dippers vibrate in phase with a period of 1.5 s to produce waves of speed 4.0 cm s−1.
(i) Determine the wavelength of the waves.
wavelength = ..................................................... cm [2]

(ii) By reference to the distances PR and QR, explain why the water particles are at rest at point R.
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(c) A wave is produced on the surface of a different liquid. At one particular time, the variation of
the vertical displacement y with distance x along the surface of the liquid is shown in Fig. 4.2.
Fig. 4.2
(i) The wave has intensity I1 at distance x = 2.0 cm and intensity I2 at x = 10.0 cm.
Determine the ratio
ratio = ......................................................... [2]
(ii) State the phase difference, with its unit, between the oscillations of the liquid particles at
distances x = 3.0 cm and x = 4.0 cm.
phase difference = .......................................................... [1]
[Total: 11]
S-16/V21/Q5
Q8 The variation with time t of the displacement y of a wave X, as it passes a point P, is shown in Fig. 5.1.
Fig. 5.1
The intensity of wave X is I.
(a) Use Fig. 5.1 to determine the frequency of wave X.
frequency = .................................................... Hz [2]
(b) A second wave Z with the same frequency as wave X also passes point P. Wave Z has intensity 2I. The phase
difference between the two waves is 90°. On Fig. 5.1, sketch the variation with time t of the displacement y of wave Z.
Show your working.
[3]
(c) A double-slit interference experiment is used to determine the wavelength of light emitted from a laser, as shown in
Fig. 5.2.

The separation of the slits is 0.45 mm. The fringes are viewed on a screen at a distance D from the double slit.
The fringe width x is measured for different distances D. The variation with D of x is shown in Fig. 5.3.
Fig. 5.3
(i) Use the gradient of the line in Fig. 5.3 to determine the wavelength, in nm, of the laser light.
wavelength = .................................................... nm [4]
(ii) The separation of the slits is increased. State and explain the effects, if any, on the graph of Fig. 5.3.
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[Total: 11]
S-16/V22/Q4
Q9 (a) By reference to the direction of the propagation of energy, state what is meant by a longitudinal
wave and by a transverse wave.
longitudinal: ........................................................................................................................................................................
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transverse: .........................................................................................................................................................................
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[2]
(b) The intensity of a sound wave passing through air is given by
Ι = Kvρ f 2A2
where Ι is the intensity (power per unit area),
K is a constant without units,
v is the speed of sound,
ρ is the density of air,
f is the frequency of the wave
and A is the amplitude of the wave.
Show that both sides of the equation have the same SΙ base units.
[3]
(c) (i) Describe the Doppler effect.
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(ii) A distant star is moving away from a stationary observer.

State the effect of the motion on the light observed from the star.
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(d) A car travels at a constant speed towards a stationary observer. The horn of the car sounds at
a frequency of 510 Hz and the observer hears a frequency of 550 Hz. The speed of sound in air is 340 m s–1.
Calculate the speed of the car.
speed = ................................................ m s–1 [3]
[Total: 10]
S-16/V22/Q5
Q10 (a) Light of a single wavelength is incident on a diffraction grating. Explain the part played by
diffraction and interference in the production of the first order maximum by the diffraction grating.
diffraction: ...........................................................................................................................................................................
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interference: .......................................................................................................................................................................
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[3]
(b) The diffraction grating illustrated in Fig. 5.1 is used with light of wavelength 486 nm.
The orders of the maxima produced are shown on the screen in Fig. 5.1. The angle between
the two second order maxima is 59.4°.
Calculate the number of lines per millimetre of the grating.
number of lines per millimetre = ................................................ mm–1 [3]
[Total: 6]
S-16/V23/Q7
Q11(a) Apparatus used to produce stationary waves on a stretched string is shown in Fig. 7.1.
Fig. 7.1
The frequency generator is switched on.
(i) Describe two adjustments that can be made to the apparatus to produce stationary waves on the string.
1. ......................................................................................................................................................................................
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2. ......................................................................................................................................................................................
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[2]
(ii) Describe the features that are seen on the stretched string that indicate stationary waves have been produced.
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(b) The variation with time t of the displacement x of a particle caused by a progressive wave R is shown in Fig. 7.2. For
the same particle, the variation with time t of the displacement x caused by a second wave S is also shown in Fig. 7.2.
Fig. 7.2
(i) Determine the phase difference between wave R and wave S. Include an appropriate unit.
phase difference = .......................................................... [1]

(ii) Calculate the ratio
ratio = .......................................................... [2]
[Total: 6]
W-16/V21/Q4
Q12 (a) State what is meant by the frequency of a progressive wave.
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(b) A cathode-ray oscilloscope (c.r.o.) is used to determine the frequency of the sound emitted by
a loudspeaker. The trace produced on the screen of the c.r.o. is shown in Fig. 4.1.
Fig. 4.1
The time-base setting of the c.r.o. is 250 μs cm–1.
Show that the frequency of the sound wave is 1600 Hz.
[2]
(c) The loudspeaker in (b) emits the sound in all directions. A person attaches the loudspeaker to a string and then swings
the loudspeaker at a constant speed in a horizontal circle above his head. An observer, standing a large distance away
from the loudspeaker, hears sound of maximum frequency 1640 Hz. The speed of sound in air is 330 m s–1.
(i) Determine the speed of the loudspeaker.
speed = ................................................ m s–1 [2]
(ii) Describe and explain, qualitatively, the variation in the frequency of the sound heard by the observer.
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[Total: 8]
W-16/V21/Q5
Q13(a) State what is meant by the diffraction of a wave.
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(b) Laser light of wavelength 500 nm is incident normally on a diffraction grating. The resulting diffraction pattern has
diffraction maxima up to and including the fourth-order maximum.
Calculate, for the diffraction grating, the minimum possible line spacing.
line spacing = ...................................................... m [3]
(c) The light in (b) is now replaced with red light. State and explain whether this is likely to result in the formation of a fifth-
order diffraction maximum.
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[Total: 7]
W-16/V22/Q4
Q14(a) State what is meant by the diffraction of a wave.
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(b) An arrangement for demonstrating the interference of light is shown in Fig. 4.1.

The wavelength of the light from the laser is 580 nm. The separation of the slits is 0.41 mm.
The perpendicular distance between the double slit and the screen is D.
Coherent light emerges from the slits and an interference pattern is observed on the screen.
The central bright fringe is produced at point X. The closest dark fringes to point X are
produced at points Y and Z. The distance XY is 2.0 mm.
(i) Explain why a bright fringe is produced at point X.
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(ii) State the difference in the distances, in nm, from each slit to point Y.
distance = .................................................... nm [1]
(iii) Calculate the distance D.
D = ...................................................... m [3]
(iv) The intensity of the light passing through the two slits was initially the same. The intensity of the light through one of
the slits is now reduced. Compare the appearance of the fringes before and after the change of intensity.
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[Total: 10]
F-17/V22/Q4
Q15(a) State what is meant by the Doppler effect.
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(b) A child sits on a rotating horizontal platform in a playground. The child moves with a constant speed along a circular
path, as illustrated in Fig. 4.1.
Fig. 4.1
An observer is standing a long distance away from the child. During one particular revolution, the child, moving at a speed
of 7.5 m s–1, starts blowing a whistle at point P and stops blowing it at point Q on the circular path. The whistle emits
sound of frequency 950 Hz. The speed of sound in air is 330 m s–1.
(i) Determine the maximum frequency of the sound heard by the distant observer.
maximum frequency = ..................................................... Hz [2]
(ii) Describe the variation in the frequency of the sound heard by the distant observer.
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[Total: 6]
S-17/V21/Q4
Q16(a) State the conditions required for the formation of stationary waves.
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(b) One end of a string is attached to a vibrator. The string is stretched by passing the other end
over a pulley and attaching a load, as illustrated in Fig. 4.1.
Fig. 4.1
The frequency of vibration of the vibrator is adjusted to 250 Hz and a transverse wave travels along the string with a
speed of 12 m s–1. The wave is reflected at the pulley and a stationary wave forms on the string.
Fig. 4.2 shows the string between points A and B at time t = t1.
Fig. 4.2
At time t = t1 the string has maximum displacement.
(i) Calculate the distance AB.
distance = .......................................................m [2]
(ii) On Fig. 4.2, sketch the position of the string between A and B at times
1. t = t1 + 2.0 ms (label this line P),
2. t = t1 + 5.0 ms (label this line Q).
[3]
[Total: 7]
S-17/V21/Q5
Q17(a) Describe the Doppler effect.
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(b) A car travels with a constant velocity along a straight road. The car horn with a frequency of
400 Hz is sounded continuously. A stationary observer on the roadside hears the sound from
the horn at a frequency of 360 Hz.
The speed of sound is 340 m s–1.
Determine the magnitude v, and the direction, of the velocity of the car relative to the observer.
v = .......................................................m s–1
direction ...............................................................
[3]
[Total: 4]
S-17/V22/Q5
Q18(a) Define the frequency of a sound wave.
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(b) A sound wave travels through air. Describe the motion of the air particles relative to the
direction of travel of the sound wave.
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(c) The sound wave emitted from the horn of a stationary car is detected with a microphone and
displayed on a cathode-ray oscilloscope (c.r.o.), as shown in Fig. 5.1.
Fig. 5.1
The y-axis setting is 5.0 mV cm–1.
The time-base setting is 0.50 ms cm–1.
(i) Use Fig. 5.1 to determine the frequency of the sound wave.
frequency = ..................................................... Hz [2]
(ii) The horn of the car sounds continuously. Describe the changes to the trace seen on the
c.r.o. as the car travels at constant speed
1. directly towards the stationary microphone,
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2. directly away from the stationary microphone.
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[3]
[Total: 7]
S-17/V22/Q6
Q19(a) Interference fringes may be observed using a light-emitting laser to illuminate a double slit. The double slit acts as
two sources of light. Explain
(i) the part played by diffraction in the production of the fringes,
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(ii) the reason why a double slit is used rather than two separate sources of light.
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(b) A laser emitting light of a single wavelength is used to illuminate slits S1 and S2, as shown in Fig. 6.1.

An interference pattern is observed on the screen AB. The separation of the slits is 0.48 mm.
The slits are 2.4 m from AB. The distance on the screen across 16 fringes is 36 mm, as illustrated in Fig. 6.2.
Fig. 6.2
Calculate the wavelength of the light emitted by the laser.
wavelength = .......................................................m [3]

(c) Two dippers D1 and D2 are used to produce identical waves on the surface of water, as illustrated in Fig. 6.3.
Point P is 7.2 cm from D1 and 11.2 cm from D2. The wavelength of the waves is 1.6 cm. The phase difference between
the waves produced at D1 and D2 is zero.
(i) State and explain what is observed at P.
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(ii) State and explain the effect on the answer to (c)(i) if the apparatus is changed so that, separately,
1. the phase difference between the waves at D1 and at D2 is 180°,
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2. the intensity of the wave from D1 is less than the intensity of that from D2.
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[2]
[Total: 10]
S-17/V23/Q5
Q20(a) A diffraction grating is used to determine the wavelength of light.
(i) Describe the diffraction of light at a diffraction grating.
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(ii) By reference to interference, explain
1. the zero order maximum,
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2. the first order maximum.
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[3]
(b) A diffraction grating is used with different wavelengths of light. The angle θ of the second
order maximum is measured for each wavelength. The variation with wavelength λ of sin θ is shown in Fig. 5.1.
Fig. 5.1
(i) Determine the gradient of the line shown in Fig. 5.1.
gradient = ...........................................................[2]
(ii) Use the gradient determined in (i) to calculate the slit separation d of the diffraction grating.
d = .......................................................m [2]
(iii) On Fig. 5.1, sketch a line to show the results that would be obtained for the first order maxima. [1]
[Total: 10]
W-17/V21/Q3
Q21 (a) State the difference between a stationary wave and a progressive wave in terms of
(i) the energy transfer along the wave,
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(ii) the phase of two adjacent vibrating particles.
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(b) A tube is open at both ends. A loudspeaker, emitting sound of a single frequency, is placed near one end of the tube,
as shown in Fig. 3.1.
Fig. 3.1
The speed of the sound in the tube is 340 m s–1. The length of the tube is 0.60 m.
A stationary wave is formed with an antinode A at each end of the tube and two antinodes inside the tube.
(i) State what is meant by an antinode of the stationary wave.
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......................................................................................................................................................................................[1]
(ii) State the distance between a node and an adjacent antinode.
distance = ...................................................... m [1]
(iii) Determine, for the sound in the tube,

1. the wavelength,
wavelength = ...................................................... m [1]
2. the frequency.
frequency = .................................................... Hz [2]

(iv) Determine the minimum frequency of the sound from the loudspeaker that produces a stationary wave in the tube.
minimum frequency = .................................................... Hz [2]
[Total: 9]
W-17/V22/Q4
Q22(a) State the conditions required for the formation of a stationary wave.
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(b) A horizontal string is stretched between two fixed points X and Y. The string is made to vibrate
vertically so that a stationary wave is formed. At one instant, each particle of the string is at its maximum displacement, as
shown in Fig. 4.1.
Fig. 4.1
P and Q are two particles of the string. The string vibrates with a frequency of 40 Hz. Distance XY is 2.0 m.
(i) State the number of antinodes in the stationary wave.
number = ...........................................................[1]
(ii) Determine the minimum time taken for the particle P to travel from its lowest point to its highest point.
time taken = ........................................................s [2]
(iii) State the phase difference, with its unit, between the vibrations of particle P and of particle Q.
phase difference = ...........................................................[1]
(iv) Determine the speed of a progressive wave along the string.
speed = ..................................................m s–1 [2]

[Total: 8]
W-17/V23/Q4
Q23(a) By reference to the direction of propagation of energy, explain what is meant by a longitudinal wave.
............................................................................................................................................................................................
.........................................................................................................................................................................................[1]
(b) A car horn emits a sound wave of frequency 800 Hz. A microphone and a cathode-ray oscilloscope (c.r.o.) are used to
analyse the sound wave. The waveform displayed on the c.r.o. screen is shown in Fig. 4.1.
Fig. 4.1
Determine the time-base setting, in s cm–1, of the c.r.o.
time-base setting = ............................................... s cm–1 [3]
(c) The intensity I of the sound at a distance r from the car horn in (b) is given by the expression
I = k/r 2 where k is a constant.
Fig. 4.2 shows the car in (b) on a road.
Fig. 4.2
An observer stands at point O. Initially the car is parked at point X which is 120 m away from
point O. The car then moves directly towards the observer and stops at point Y, a distance of 30 m away from O.
The car horn continuously emits sound when the car is moving between points X and Y.
(i) The sound wave at point O has amplitude AX when the car is at X and has amplitude AY when the car is at Y.
Calculate the ratio : AY / AX

.
ratio = ...........................................................[3]
(ii) When the car is parked at X, the frequency of the sound from the horn that is detected by the observer is 800 Hz. As
the car moves from X to Y, the maximum change in the detected frequency is 16 Hz.
The speed of the sound in air is 330 m s–1.
Determine, to two significant figures,
1. the minimum wavelength of the sound detected by the observer,
wavelength = ...................................................... m [2]
2. the maximum speed of the car.
speed = ................................................. m s–1 [2]
[Total: 11]
F-17/V22/Q4
Q24 (a) State the conditions required for the formation of a stationary wave.
............................................................................................................................................................................................
............................................................................................................................................................................................
............................................................................................................................................................................................
........................................................................................................................................................................................[2]
(b) The sound from a loudspeaker is detected by a microphone that is connected to a cathode-ray oscilloscope (c.r.o.).
Fig. 4.1 shows the trace on the screen of the c.r.o.
Fig. 4.1
In air, the sound wave has a speed of 330 m s–1 and a wavelength of 0.18 m.
(i) Calculate the frequency of the sound wave.
frequency = .................................................... Hz [2]

(ii) Determine the time-base setting, in s cm–1, of the c.r.o.
time-base setting = ............................................... s cm–1 [2]
(iii) The intensity of the sound from the loudspeaker is now halved. The wavelength of the sound is unchanged.
Assume that the amplitude of the trace is proportional to the amplitude of the sound wave.
On Fig. 4.1, sketch the new trace shown on the screen of the c.r.o. [2]
(c) The loudspeaker in (b) is held above a vertical tube of liquid, as shown in Fig. 4.2.
Fig. 4.2 Fig. 4.3

A tap at the bottom of the tube is opened so that liquid drains out at a constant rate. The
wavelength of the sound from the loudspeaker is 0.18 m. The sound that is heard first
becomes much louder when the liquid surface reaches level A. The next time that the sound
becomes much louder is when the liquid surface reaches level B, as shown in Fig. 4.3.
(i) Calculate the vertical distance between level A and level B.
distance = ...................................................... m [1]
(ii) On Fig. 4.3, label with the letter N the positions of the nodes of the stationary wave that is
formed in the air column when the liquid surface is at level B. [1]
(iii) The mass of liquid leaving the tube per unit time is 6.7 g s–1. The tube has an internal
cross-sectional area of 13 cm2. The density of the liquid is 0.79 g cm–3.
Calculate the time taken for the liquid to move from level A to level B.
time = ....................................................... s [2]
[Total: 12]
S-18/V21/Q4
Q25 (a) For a progressive wave, state what is meant by
(i) the period,
............................................................................................................................................................................................
........................................................................................................................................................................................[1]
(ii) the wavelength.
...........................................................................................................................................................................................
........................................................................................................................................................................................[1]
(b) Fig. 4.1 shows the variation with time t of the displacement x of two progressive waves P and Q passing the same
point.
Fig. 4.1
The speed of the waves is 20 cm s–1.
(i) Calculate the wavelength of the waves.
wavelength = .................................................... cm [2]
(ii) Determine the phase difference between the two waves.
phase difference = ....................................................... ° [1]

(iii) Calculate the ratio
ratio = .......................................................... [2]

(iv) The two waves superpose as they pass the same point. Use Fig. 4.1 to determine the resultant displacement
at time t = 0.45 s.
displacement = ................................................... mm [1]
[Total: 8]
S-18/V21/Q4
Q26(a) When monochromatic light is incident normally on a diffraction grating, the emergent light
waves have been diffracted and are coherent.
Explain what is meant by
(i) diffracted waves,
.........................................................................................................................................................................................
......................................................................................................................................................................................[1]
(ii) coherent waves.
........................................................................................................................................................................................
.....................................................................................................................................................................................[1]
(b) Light consisting of only two wavelengths λ1 and λ2 is incident normally on a diffraction grating.
The third order diffraction maximum of the light of wavelength λ1 and the fourth order
diffraction maximum of the light of wavelength λ2 are at the same angle θ to the direction of the incident light.
(i) Show that the ratio λ2/λ1 is 0.75.
Explain your working.
[2]
(ii) The difference between the two wavelengths is 170 nm.
Determine wavelength λ1.
λ1 = .................................................... nm [1]
[Total: 5]
S-18/V22/Q4
Q27(a) (i) Define the wavelength of a progressive wave.
............................................................................................................................................................................................
........................................................................................................................................................................................[1]
(ii) State what is meant by an antinode of a stationary wave.
……………………….........................................................................................................................................................
......................................................................................................................................................................................[1]
(b) A loudspeaker producing sound of constant frequency is placed near the open end of a pipe, as shown in Fig. 4.1.
Fig. 4.1
A movable piston is at distance x from the open end of the pipe. Distance x is increased from
x = 0 by moving the piston to the left with a constant speed of 0.75 cm s–1.
The speed of the sound in the pipe is 340 m s–1.
(i) A much louder sound is first heard when x = 4.5 cm. Assume that there is an antinode of
a stationary wave at the open end of the pipe.
Determine the frequency of the sound in the pipe.
frequency = ..................................................... Hz [3]
(ii) After a time interval, a second much louder sound is heard. Calculate the time interval
between the first louder sound and the second louder sound being heard.
time interval = ........................................................s [2]
[Total: 7]
S-18/V23/Q5
Q28(a) State the relationship between the intensity and the amplitude of a wave.
..........................................................................................................................................................................................
.......................................................................................................................................................................................[1]
(b) Microwaves of the same amplitude and wavelength are emitted in phase from two sources P and Q. The sources are
arranged as shown in Fig. 5.1.
Fig. 5.1
A microwave detector is moved along a path that is parallel to the line joining P and Q. A series of intensity maxima and
intensity minima are detected. When the detector is at a point X, the distance PX is 1.840 m and the distance QX is 2.020
m. The microwaves have a wavelength of 6.0 cm.
(i) Calculate the frequency of the microwaves.
frequency = .................................................... Hz [2]
(ii) Describe and explain the intensity of the microwaves detected at X.
............................................................................................................................................................................................
............................................................................................................................................................................................
............................................................................................................................................................................................
............................................................................................................................................................................................
........................................................................................................................................................................................[3]
(iii) Describe the effect on the interference pattern along the path of the detector due to each of the following separate
changes.
1. The wavelength of the microwaves decreases.
...........................................................................................................................................................................................
...........................................................................................................................................................................................
2. The phase difference between the microwaves emitted from the sources changes to 180°.
............................................................................................................................................................................................
............................................................................................................................................................................................
[2]
[Total: 8]
W-18/V21/Q5
Q29 (a) State the principle of superposition.
...........................................................................................................................................................................................
...........................................................................................................................................................................................
....................................................................................................................................................................................... [2]
(b) An arrangement for demonstrating the interference of light is shown in Fig. 4.1.

The wavelength of the light is 610 nm. The distance between the double slit and the screen is 2.7 m.
An interference pattern of bright fringes and dark fringes is observed on the screen. The
centres of the bright fringes are labelled B and centres of the dark fringes are labelled D.
Point P is the centre of a particular dark fringe and point Q is the centre of a particular bright
fringe, as shown in Fig. 4.1. The distance across five bright fringes is 22 mm.
(i) The light waves leaving the two slits are coherent.
State what is meant by coherent.
.........................................................................................................................................................................................
..................................................................................................................................................................................... [1]
(ii) 1. State the phase difference between the waves meeting at Q.
phase difference = .............................................................. °
2. Calculate the path difference, in nm, of the waves meeting at P.
path difference = ......................................................... nm

[2]
(iii) Determine the distance a between the two slits.
a = ...................................................... m [3]
(iv) A higher frequency of visible light is now used. State and explain the change to the separation of the fringes.
..........................................................................................................................................................................................
...................................................................................................................................................................................... [1]
(v) The intensity of the light incident on the double slit is now increased without altering its frequency. Compare the
appearance of the fringes after this change with their appearance before this change.
..........................................................................................................................................................................................
..........................................................................................................................................................................................
..........................................................................................................................................................................................
...................................................................................................................................................................................... [2]
[Total: 11]
W-18/V22/Q4
Q30(a) Sound waves are longitudinal waves. By reference to the direction of propagation of energy,
state what is meant by a longitudinal wave.
.........................................................................................................................................................................................
......................................................................................................................................................................................[1]
(b) A stationary sound wave in air has amplitude A. In an experiment, a detector is used to determine A2. The variation of
A2 with distance x along the wave is shown in Fig. 4.1.
Fig. 4.1
(i) State the phase difference between the vibrations of an air particle at x = 25 cm and the
vibrations of an air particle at x = 50 cm.

(ii) The speed of the sound in the air is 330 m s–1. Determine the frequency of the sound wave.
frequency = .................................................... Hz [3]
(iii) Determine the ratio
ratio = ...........................................................[2]
[Total: 7]
W-18/V22/Q5
Q31 Red light of wavelength 640 nm is incident normally on a diffraction grating having a line spacing of 1.7 × 10–6 m, as
shown in Fig. 5.1.

The second order diffraction maximum of the light is at an angle θ to the direction of the incident light.
(a) Show that angle θ is 49°.
[3]
(b) Determine a different wavelength of visible light that will also produce a diffraction maximum
at an angle of 49°.
wavelength = ...................................................... m [2]

[Total: 5]
W-18/V23/Q4
Q32(a) On Fig. 4.1, complete the two graphs to illustrate what is meant by the amplitude A, the wavelength λ and the
period T of a progressive wave. Ensure that you label the axes of each graph.
Fig. 4.1
[3]
(b) A horizontal string is stretched between two fixed points X and Y. A vibrator is used to oscillate
the string and produce a stationary wave. Fig. 4.2 shows the string at one instant in time.
Fig. 4.2
The speed of a progressive wave along the string is 30 m s–1. The stationary wave has a period of 40 ms.
(i) Explain how the stationary wave is formed on the string.
...........................................................................................................................................................................................
...........................................................................................................................................................................................
...........................................................................................................................................................................................
.......................................................................................................................................................................................[2]
(ii) A particle on the string oscillates with an amplitude of 13 mm. At time t, the particle has zero displacement.
Calculate
1. the displacement of the particle at time (t + 100 ms),
displacement = ........................................................ mm
2. the total distance moved by the particle from time t to time (t + 100 ms).
distance = ........................................................ mm
[3]
(iii) Determine
1. the frequency of the wave,
frequency = ..................................................... Hz [1]

2. the horizontal distance from X to Y.
distance = ...................................................... m [3]
[Total: 12]
F-19/V22/Q5
Q33(a) By reference to two waves, state:
(i) the principle of superposition
...........................................................................................................................................................................................
...........................................................................................................................................................................................
..........................................................................................................................................................................................
.........................................................................................................................................................................................[2]
(ii) what is meant by coherence.
…………………………………….........................................................................................................................................
.........................................................................................................................................................................................[1]
(b) Two coherent waves P and Q meet at a point in phase and superpose. Wave P has an
amplitude of 1.5 cm and intensity I. The resultant intensity at the point where the waves meet is 3I.
Calculate the amplitude of wave Q.
amplitude = .................................................... cm [2]
(c) The apparatus shown in Fig. 5.1 is used to produce an interference pattern on a screen.
Light of wavelength 680 nm is incident on a double-slit. The slit separation is a. The

separation between adjacent fringes is x. Fringes are viewed on a screen at distance D from the double-slit.
Distance D is varied from 2.0 m to 3.5 m. The variation with D of x is shown in Fig. 5.2.
Fig. 5.2
(i) Use Fig. 5.2 to determine the slit separation a.
a = ...................................................... m [3]
(ii) The laser is now replaced by another laser that emits light of a shorter wavelength.
On Fig. 5.2, sketch a possible line to show the variation with D of x for the fringes that are now produced. [2]
[Total: 10]
S-19/V21/Q5
Q34(a) A loudspeaker oscillates with frequency f to produce sound waves of wavelength λ. The
loudspeaker makes N oscillations in time t.
(i) State expressions, in terms of some or all of the symbols f, λ and N, for:
1. the distance moved by a wavefront in time t
distance = ...............................................................
2. time t.
time t = ...............................................................
[2]
(ii) Use your answers in (i) to deduce the equation relating the speed v of the sound wave to f and λ.
[1]
(b) The waveform of a sound wave is displayed on the screen of a cathode-ray oscilloscope (c.r.o.), as shown in Fig. 5.1.
Fig. 5.1
The time-base setting is 0.20 ms cm−1.
Determine the frequency of the sound wave.
frequency = .................................................... Hz [2]
(c) Two sources S1 and S2 of sound waves are positioned as shown in Fig. 5.2.

The sources emit coherent sound waves of wavelength 0.85 m. A sound detector is moved
parallel to the line S1S2 from a point X to a point Y. Alternate positions of maximum loudness
L and minimum loudness Q are detected, as illustrated in Fig. 5.2.
Distance S1X is equal to distance S2X. Distance S2Y is 7.40 m.
(i) Explain what is meant by coherent waves.
..........................................................................................................................................................................................
.......................................................................................................................................................................................[1]
(ii) State the phase difference between the two waves arriving at the position of minimum
loudness Q that is closest to point X.
(iii) Determine the distance S1Y.
distance = ...................................................... m [2]
[Total: 9]
S-19/V22/Q5
Q35(a) For a progressive water wave, state what is meant by:
(i) displacement
..........................................................................................................................................................................................
......................................................................................................................................................................................[1]
(ii) amplitude.
..........................................................................................................................................................................................
…………………………………........................................................................................................................................[1]
(b) Two coherent waves X and Y meet at a point and superpose. The phase difference between
the waves at the point is 180°. Wave X has an amplitude of 1.2 cm and intensity I. Wave Y has an amplitude of 3.6 cm.
Calculate, in terms of I, the resultant intensity at the meeting point.
intensity = .......................................................... [2]
(c) (i) Monochromatic light is incident on a diffraction grating. Describe the diffraction of the
light waves as they pass through the grating.
............................................................................................................................................................................................
............................................................................................................................................................................................
.......................................................................................................................................................................................[2]
(ii) A parallel beam of light consists of two wavelengths 540 nm and 630 nm. The light is
incident normally on a diffraction grating. Third-order diffraction maxima are produced for
each of the two wavelengths. No higher orders are produced for either wavelength.
Determine the smallest possible line spacing d of the diffraction grating.
d = ...................................................... m [3]
(iii) The beam of light in (c)(ii) is replaced by a beam of blue light incident on the same diffraction grating.
State and explain whether a third-order diffraction maximum is produced for this blue light.
...........................................................................................................................................................................................
...........................................................................................................................................................................................
.......................................................................................................................................................................................[2]
[Total: 11]
S-19/V23/Q5
Q36 A vertical tube of length 0.60 m is open at both ends, as shown in Fig. 5.1.
Fig. 5.1
An incident sinusoidal sound wave of a single frequency travels up the tube. A stationary wave
is then formed in the air column in the tube with antinodes A at both ends and a node N at the midpoint.
(a) Explain how the stationary wave is formed from the incident sound wave.
.........................................................................................................................................................................................
.........................................................................................................................................................................................
..........................................................................................................................................................................................
......................................................................................................................................................................................[2]
(b) On Fig. 5.2, sketch a graph to show the variation of the amplitude of the stationary wave with height h above the
bottom of the tube.
Fig. 5.2 [2]
(c) For the stationary wave, state:

(i) the direction of the oscillations of an air particle at a height of 0.15 m above the bottom of the tube
.......................................................................................................................................................................................[1]
(ii) the phase difference between the oscillations of a particle at a height of 0.10 m and a particle at a height of 0.20 m
above the bottom of the tube.
phase difference = ........................................................ ° [1]

(d) The speed of the sound wave is 340 m s−1.
Calculate the frequency of the sound wave.
frequency = .................................................... Hz [2]
(e) The frequency of the sound wave is gradually increased.

Determine the frequency of the wave when a stationary wave is next formed.
frequency = .................................................... Hz [1]
[Total: 9]
W-19/V21/Q5
Q37 A ripple tank is used to demonstrate the interference of water waves.
Two dippers D1 and D2 produce coherent waves that have circular wavefronts, as illustrated in
Fig. 5.1.
Fig. 5.1
The lines in the diagram represent crests. The waves have a wavelength of 6.0 cm.
(a) One condition that is required for an observable interference pattern is that the waves must be coherent.
(i) Describe how the apparatus is arranged to ensure that the waves from the dippers are coherent.
............................................................................................................................................................................................
.......................................................................................................................................................................................... [1]
(ii) State one other condition that must be satisfied by the waves in order for the interference pattern to be observable.
............................................................................................................................................................................................
........................................................................................................................................................................................ [1]
(b) Light from a lamp above the ripple tank shines through the water onto a screen below the tank. Describe one way of
seeing the illuminated pattern more clearly.
..........................................................................................................................................................................................
...................................................................................................................................................................................... [1]
(c) The speed of the waves is 0.40 m s–1. Calculate the period of the waves.
period = ...................................................... s [2]
(d) Fig. 5.1 shows a point X that lies on a crest of the wave from D1 and midway between two
adjacent crests of the wave from D2.
For the waves at point X, state:
(i) the path difference, in cm
path difference = ................................................... cm [1]
(ii) the phase difference.
phase difference = ....................................................... [1]
(e) On Fig. 5.1, draw one line, at least 4 cm long, which joins points where only maxima of the
interference pattern are observed. [1]
[Total: 8]
W-19/V22/Q5
Q38(a) State what is meant by the wavelength of a progressive wave.
...........................................................................................................................................................................................
....................................................................................................................................................................................... [1]
(b) A cathode-ray oscilloscope (CRO) is used to analyse a sound wave. The screen of the CRO is shown in Fig. 5.1
Fig. 5.1
The time-base setting of the CRO is 2.5 ms cm–1.
Determine the frequency of the sound wave.
frequency = .................................................... Hz [2]

(c) The source emitting the sound in (b) is at point A. Waves travel from the source to point C
along two different paths, AC and ABC, as shown in Fig. 5.2.

Distance AB is 8.0 m and distance AC is 20.8 m. Angle ABC is 90°. Assume that there is no phase change of the sound
wave due to the reflection at point B. The wavelength of the waves is 1.6 m.
(i) Show that the waves meeting at C have a path difference of 6.4 m.
[1]
(ii) Explain why an intensity maximum is detected at point C.
..........................................................................................................................................................................................
..........................................................................................................................................................................................
..................................................................................................................................................................................... [2]
(iii) Determine the difference between the times taken for the sound to travel from the source
to point C along the two different paths.
time difference = ....................................................... s [2]
(iv) The wavelength of the sound is gradually increased. Calculate the wavelength of the sound when an intensity
maximum is next detected at point C.
wavelength = ......................................................m [1]
[Total: 9]
W-19/V23/Q5
Q39(a) Light waves emerging from the slits of a diffraction grating are coherent and produce an interference pattern.
Explain what is meant by:
(i) coherence
..........................................................................................................................................................................................
...................................................................................................................................................................................... [1]
(ii) interference.
...........................................................................................................................................................................................
....................................................................................................................................................................................... [1]
(b) A narrow beam of light from a laser is incident normally on a diffraction grating, as shown inFig. 5.1.

Spots of light are seen on a screen positioned parallel to the grating. The angle corresponding
to each of the second order maxima is 51°. The number of lines per unit length on the
diffraction grating is 6.7 × 105 m–1.
(i) Determine the wavelength of the light.
wavelength = ..................................................... m [2]
(ii) State and explain the change, if any, to the distance between the second order maximum
spots on the screen when the light from the laser is replaced by light of a shorter wavelength.
............................................................................................................................................................................................
............................................................................................................................................................................................
........................................................................................................................................................................................[1]
[Total: 5]
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
Q20
Q21
Q22
Q23
Q24
Q25
Q26
Q27
Q28
Q29
Q30
Q31
Q32
Q33
Q34
Q35
Q36
Q37
Q38
Q39

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AS- PHYSICS-WORK-SHEET MD.

Fig. 6.1 (not to scale)

number = .......................................................... [3]

frequency = ................................................. GHz [3]

frequency = .................................................... Hz [2]

(iii) State the phase difference between the waves.

phase difference = ........................................................ ° [1]

Fig. 6.2 (not to scale)

distance = ...................................................... m [3]

phase difference = ......................... unit .................... [1]

Fig. 7.1 (view from above)

amplitude = ................................................... mm [1]

(ii) the wavelength of the wave.

wavelength = ................................................... mm [1]

(ii) Explain why D1 and D2 are connected to the same motor.

Fig. 2.2 Fig. 2.3 Fig. 2.4

Fig. 2.5 [3]

(ii) State the principle of superposition.

Fig. 4.1 (not to scale)

wavelength = ..................................................... cm [2]

ratio = ......................................................... [2]

phase difference = .......................................................... [1]

frequency = .................................................... Hz [2]

Fig. 5.2 (not to scale)

wavelength = .................................................... nm [4]

(ii) A distant star is moving away from a stationary observer.

speed = ................................................ m s–1 [3]

number of lines per millimetre = ................................................ mm–1 [3]

phase difference = .......................................................... [1]

ratio = .......................................................... [2]

speed = ................................................ m s–1 [2]

line spacing = ...................................................... m [3]

Fig. 4.1 (not to scale)

distance = .................................................... nm [1]

(iii) Calculate the distance D.

maximum frequency = ..................................................... Hz [2]

distance = .......................................................m [2]

frequency = ..................................................... Hz [2]

2. directly away from the stationary microphone.

Fig. 6.1 (not to scale)

Calculate the wavelength of the light emitted by the laser.

wavelength = .......................................................m [3]

Fig. 6.3 (not to scale)

2. the first order maximum.

(i) Determine the gradient of the line shown in Fig. 5.1.

(ii) the phase of two adjacent vibrating particles.

(ii) State the distance between a node and an adjacent antinode.

distance = ...................................................... m [1]

(iii) Determine, for the sound in the tube,

wavelength = ...................................................... m [1]

frequency = .................................................... Hz [2]

minimum frequency = .................................................... Hz [2]

time taken = ........................................................s [2]

phase difference = ...........................................................[1]

(iv) Determine the speed of a progressive wave along the string.

speed = ..................................................m s–1 [2]

Determine the time-base setting, in s cm–1, of the c.r.o.

time-base setting = ............................................... s cm–1 [3]

Calculate the ratio : AY / AX