?

Wave Motion
(Practice Questions)

Properties of Waves 9. For a transverse wave travelling along a straight line, the distance
between two peaks (crests) is 5m, while the distance between one
crest and one trough is 1.5m. The possible wavelengths (in m) of
1. When a wave propagating through a medium encounters a change the waves are:
in medium, then which of the following property remains same?
1 1 1 1
(a) Speed (b) Amplitude (a) 1, 3, 5, (b) , , ,
1 3 5 4
(c) Frequency (d) Wavelength
(c) 1 1 1 1 (d) 1, 2, 3,
2. The waves which cannot travel without medium are- , , ,
2 4 6 4
(a) X-rays (b) Radio waves
(c) Light waves (d) Sound waves 10. Which one of the following statements is true?
3. Which of the following phenomenon cannot take place with sound (a) Both light and sound waves in air are transverse.
waves? (b) The sound waves in air are longitudinal while the light waves
(a) Polarisation (b) Refraction are transverse.
(c) Diffraction (d) Reflection (c) Both light and sound waves in air are longitudinal.
4. The speed of sound in air is independent from its- (d) Both light and sound waves can travel in vacuum.
(a) Amplitude (b) Frequency
(c) Phase (d) All of these
5. The frequency of a mechanical wave is 256 Hz. Calculate its Wave Equation
wavelength when its speed is 512 m/s.
11. The equation of travelling wave is given by (all quantities are in SI
units) y = 0.02 sin 2p(10t – 5x)
Type of Waves
Column-I Column-II
6. Given below are two statements: (i) Speed of wave A. 20p
Statement-I: Mechanical transverse waves cannot be generated in
(ii) Angular frequency of wave B. 0.4p
gaseous medium. (iii) Wavelength of wave C. 2
Statement-II: Mechanical transverse waves can be produced
(iv) Maximum particle speed D. 0.2
only in such medium which have shearing property. (a) i→C, ii→A, iii→D, iv→C
(a) Both statement-I and statement-II are correct. (b) i→A, ii→B, iii→C, iv→D
(b) Statement-I is correct and statement-II is incorrect. (c) i→C, ii→B, iii→A, iv→D
(c) Statement-I is is incorrect and statement-II is correct. (d) i→C, ii→A, iii→D, iv→B
(d) Both statement-I and statement-II are incorrect. 12. In a resonance tube experiment, a close organ pipe of length 120
7. An earthquake generates both transverse (S) and longitudinal (P) cm resonate when tuned with a tuning fork of frequency 340 Hz.
sound waves in the earth. The speed of S waves is about 4.5 km/s If water is poured in the pipe then (given vair = 340m/sec.):
and that of P waves is about 8.0 km/s. A seismograph records P
and S waves from an earthquake. The first P wave arrives 4.0 min A. Minimum length of water column to have the resonance is
before the first S wave. The epicentre of the earthquake is located 45 cm.
at distance about- B. The distance between two successive nodes is 50 cm.
(a) 25 km (b) 250 km C. The maximum length of water column to create the resonance
(c) 2500 km (d) 5000 km is 95 cm.
8. It is possible to distinguish between the transverse and longitudinal D. None of these.
waves by studying the property of- Choose the correct statements:
(a) Interference (b) Diffraction (a) 1, 2, 3 (b) 2, 3
(c) Reflection (d) Polarisation (c) 1, 3 (d) None
13. The equation for the displacement of a stretched string is given by 5
 t x  21. The wave function of a pulse is given by y = , where
y = 4 sin2p  −  where y and x are in cm and t in second. (4 x + 6t ) 2
 0.02 100  x and y are in metre and t is in second. The velocity of pulse is in
Column-I Column-II second. The velocity of pulse is-
(a) 2 m/s (b) 6 m/s
A. Amplitude of wave in cm P 50
B. Frequency of wave in Hz Q 4 (c) 1.5 m/s (d) 3 m/s
C. Velocity of wave in ms–1 R 4p y
22. A wave is represented by x = 4 cos (8t – ), where x and y are in
D. Maximum particle velocity in cm/s S 5000 2
T 400p metre and t in second. The frequency of the wave (in s–1)
(a) A→Q; B→P; C→P; D→T 4 8 2 π
(a) (b) (c) (d)
(b) A→R; B→S; C→P; D→T π π π 4
(c) A→Q; B→P; C→S; D→T π π 
(d) A→R; B→S; C→S; D→T 23. A travelling wave in a string is represented by y = 3 sin  t − x  .
2 4 
14. A transverse wave travels along x-axis. The particles of medium The phase difference between two particles separated by a distance
move: 4 cm is (Take x and y in cm and t in seconds)
(a) Along x-axis π π
(a) rad (b) rad
(b) Along y-axis 2 4
(c) Either along y-axis or z-axis (c) p rad (d) 0
(d) Either along y-axis or x-axis 24. In sine wave, minimum distance between 2 particles which always
15. Which of the following equations represents a transverse wave have same speed is-
travelling along –y axis?
λ λ λ
(a) x = A sin (wt – ky) (b) x = A sin (wt + ky) (a) (b) (c) (d) l
2 4 3
(c) y0 = A sin (wt – ky) (d) y0 = A sin (wt + ky)
25. The equation of a simple harmonic progressive wave is given by y
16. A plane progressive wave propagating along positive x-axis is-
= A sin(100pt – 3x). Find the distance between 2 particles having
(a) y = A sin (wt + kx) (b) y = A sin (wt – kx)
π
(c) y = A sin wt sin kx (d) y = A [sin wt] kx a phase difference of .
3
17. The equation of the progressive wave, where t is the time in π π
 x (a) (b)
second, x is the distance in metre is y = A cos 24  t −  , then 9 18
speed of wave?  12  π π
(c) (d)
18. A wave travelling in the positive x-direction having displacement 6 3
1  t X 
along y-direction as 1 m, wavelength 2pm and frequency of Hz 26. A wave is represented by y = 3 sin 2p  −  cm. The
π  0.04 0.01 
is represented by-
frequency of the wave and the maximum acceleration under this
(a) y = sin(2px – 2pt) (b) y = sin(10px – 20pt) frequency are-
(c) y = sin(2px + 2pt) (d) y = sin(x – 2t)
(a) 25 Hz, 7.5 × 104 cm/s2 (b) 100 Hz, 4.5 × 103 cm/s2
19. The equation of the progressive wave, where t is the time in
x (c) 50 Hz, 7.5 × 103 cm/s2 (d) 25 Hz, 4.5 × 104 cm/s2
second, x is the distance in metre is y = A cos 240(t – ). The
12 27. A travelling wave is described by the equation y = A sin 2p
phase difference (in SI units) between two positions 0.5 m apart is- (nt – x/l0). The maximum particle velocity is equal to 3 times the
(a) 40 (b) 20 wave velocity if-
(c) 10 (d) 5 πA 2π A
(a) l0 = (b) l0 =
20. A transverse pulse is shown in the figure, on which 4 points are 3 3
shown at any instant. Which of the following points are in a state (c) l0 = p A (d) l0 = 3p A
to move upwards in subsequent time?
28. A transverse wave is represented by y = 2sin (wt – kx) cm. The
value of wavelength (in cm) for which the wave velocity becomes
wave (+ve) equal to the maximum particle velocity will be:
(a) 4p (b) 2p
B
(c) p (d) 2
A  
29. If u is instantaneous velocity of particle and v is, velocity of
D wave, then
C  
(a) u is perpendicular to v
 
(b) u is parallel to v
 
(a) A, B (b) A, D (c) | u | is equal to | v |
(c) B, C (d) B, D  
(d) | u | = (slope of wave form) | v |

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2 Class Question Bank
 30. Which one of the following represents a wave? Transverse Wave in a String
(a) y = A sin (wt – kx)
(b) y = A cos2 (at – bx + c) + A sin2 (at – bx + c) 39. A metallic wire of 1 m length has a mass of 10 × 10–3 kg. If a tension
(c) y = A sin kx of 100 N is applied to a wire, what is the speed of transverse wave?
(d) y = A sin wt (a) 100 m/s (b) 10 m/s
31. Which of the following functions for y can never represent a (c) 200 m/s (d) 0.1 m/s
travelling wave?
40. Calculate the velocity of the transverse wave in a string which is
 ( x + vt )  stretched by a load of 15 kg. The mass of the string is 3 × 10–2 kg
A. (x2 – vt)2 B. log  
 x0  and its length is 2 m.
2 1 41. A uniform rope of length L and mass m1 hangs vertically from a
 (x + vt 
C. −  D. x + vt rigid support. A block of mass m2 is attached to the free end of the
 x0 
e rope. A transverse pulse of wavelength l1 is produced at the lower
(a) Only 1 (b) 2 and 3 end of the rope. The wavelength of the pulse when it reaches the
top of the rope is l2. The ratios is l2/l1 is-
(c) 3 and 4 (d) Only 3
32. A sinusoidal wave of frequency 500 Hz has a speed of 350 m/s. m1 + m2 m1
(a) (b)
The phase difference between two displacements at a certain point m1 m2
at times 1 ms apart is-
m1 + m2 m2
π π 3π (c) (d)
(a) (b) (c) p (d) m2 m1
4 2 2
42. The extension in a string, obeying Hooke's law is x. The speed of
 x
33. The equation of travelling wave is y = a sin 2p  pt −  . Then the transverse wave in the stretched string is V. If the extension in the
 5  string is increased to 1.5x the speed of the Transverse wave.
ratio of maximum particle velocity to wave velocity is-
(a) 1.22 V (b) 0.61 V
πa 2πa 2πa
(a) (b) 2 5πa (c) (d) (c) 1.50 V (d) 0.75 V
5 5 5
43. A steel wire 100 cm long has a mass of 10gm. If the wire is under
4 a tension of 400 N, what is the speed of transverse waves in the
34. A travelling wave pulse is given by y = 2 2
3 x + 48t + 24 xt + 2 wire?
where x and y are in metre and t is in second. The velocity of wave
is- T M
Hint : v = where m =
µ L
(a) 4 m/s (b) 2 m/s
44. A pulse is generated at lower end of a hanging rope of uniform
(c) 8 m/s (d) 12 m/s
density and length L. The speed of the pulse when it reaches the
35. The ratio of maximum particle velocity to wave velocity is [where
mid point of rope is-
symbols have their usual meanings]
(a) kA (b) Aw (c) kw (d) w/k
36. A transverse wave propagating along x-axis is represented by:
π
y(x, t) = 8 sin (0.5px – 4pt – ) where x is in metres and t is in
2
seconds. The speed of the wave is-
L
(a) 4 p m/s (b) 0.5 p m/s
π
(c) m/s (d) 8 m/s
4
37. A wave in a string has an amplitude of 2 cm. The wave travels in
the positive direction of x-axis with a speed of 128 m/s and it is
noted that 5 complete waves fit in 4 m length of the string. The (a) 2gL (b) gL
equation describing the waves is-
gL gL
(a) y = (0.02) m sin (15.7 x + 2010t) (c) (d)
2 2
(b) y = (0.02) m sin (15.7 x – 2010t) 45. A transverse pulse generated at the bottom of a uniform rope of
(c) y = (0.02) m sin (7.85 x + 1005t) length L, travels in upward direction. The time taken by it to travel
(d) y = (0.02) m sin (7.85 x – 1005t) the full length of rope will be-
38. A transverse wave is represented by y = A sin (wt – kx). For 2L
L
what value of the wavelength is the wave velocity equal to the (a) (b)
2g g
maximum particle velocity?
πA L 4L
(a) (b) pA (c) 2pA (d) A (c) (d)
2 g g

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46. A rope of length L and mass M hangs freely from the ceiling. If the 56. The speed of longitudinal mechanical wave in a material is 4200
time taken by a transverse wave to travel from the bottom to the m/s. Young's modulus of the material is 15 × 109 N/m2. What is the
top of the rope is T, then time to cover first half length is- density of the material?
 2 −1 57. Speed of sound wave in a gas is v1 and rms speed of molecules of
(a) T (b) T   the gas at the same temperature is v2. Then
 2 
 (a) v1 = v2 (b) v1 < v2
T T (c) v1 > v2 (d) v1 ≤ v2
(c) (d)
2 2 58. If at STP, velocity of sound in a gas (g= 1.5) is 600 m/s, the r.m.s.
47. A uniform rope having some mass hangs vertically from a rigid Velocity of the gas molecules at STP will be-
support. A transverse wave pulse is produced at the lower end. The (a) 400 m/s (b) 600 m/s
speed (u) of the wave pulse varies with height (h) from the lower
(c) 600 2 m/s (d) 300 2 m/s
end as-
u u 59. The speed of sound in air at NTP is 332 m/s. Calculate the
percentage error in speed of sound as calculated from Newton's
formula. Given that the density of air is 1.293 kg/m3.
(a) (b) 60. The speed of sound in hydrogen at NTP, is 1270 m/s. Then the
speed in a mixture of hydrogen and oxygen in the ratio 4:1 by
volume, (in m/s) will be-

h (a) 635 (b) 318

h
u (c) 158 (d) 1270
u
61. The ratio of speed of sound in hydrogen gas to the speed of sound
in oxygen gas at the same temperature is-
(a) 4 : 1 (b) 1 : 2
(c) (d)
(c) 1 : 4 (d) 1 : 1
62. Oxygen is 16 times heavier than hydrogen. Equal volume of
hydrogen and oxygen are mixed. The ratio of speed of sound in
h h
the mixture to that in hydrogen is-
48. Two strings of same material are stretched to the same tension. If
their radii are in the ratio 1 : 2, then respective wave velocities in 2
(a) 8 (b)
them will be in ratio- 17
(a) 4 : 1 (b) 2 : 1 (c) 1 : 2 (d) 1 : 4 1 32
(c) (d)
49. A copper wire is held at the two ends by rigid supports. At 50°C 8 17
the wire is just taut, with negligible tension. If Y = 1.2 × 1011 N/
m2, a = 1.6 × 10–5 / °C and r = 9.2 × 103 kg/m3, then the speed of 63. The speed of sound waves in air at 300 K is 332 m/s. At what
transverse waves in this wire at 30°C is- temperature will the speed be 574 m/s?

(a) 64.6 m/s (b) 16.2 m/s 64. Regarding speed of sound in gas match the following-
(c) 23.2 m/s (d) 32.2 m/s Column-I Column-II
50. The percentage increase in the speed of transverse waves produced
(i) Temperature of gas is made 4 A. Speed becomes
in a stretched string if the tension is increased by 4%, will be
times and pressure 2 times 2 2 times
_________%.
(ii) Only pressure is made 4 times B. Speed becomes
without change in temperature two times
(iii) Only temperature changed to C. Speed remain
Sound Wave 4 times unchanged
(iv) Molecular mass of the gas is D. Speed become
51. At constant temperature if pressure becomes double then speed of
made 4 times half
sound will be?
(a) i→A, ii→C, iii→D, iv→B
52. If pressure becomes double at constant density, then speed of
(b) i→B, ii→C, iii→D, iv→A
sound will be ?
(c) i→B, ii→C, iii→B, iv→D
53. Calculate the speed of the longitudinal wave in steel. Young's
(d) i→C, ii→B, iii→A, iv→C
modulus for steel is 3 × 1010 N / m2 and its density is 1.2 × 103 kg/m3.
65. The velocity of sound in air at 20°C is 340 m s–1. Keeping the
54. If the speed of longitudinal mechanical waves in water is 1400 temperature constant, what will be the velocity of sound in air
m/s then calculate the Bulk modulus of elasticity of water. when the pressure of the gas is doubled?
(given density of water is 1 g/cm3).
66. Calculate the speed of sound in hydrogen at N.T.P., if density of
55. The wavelength of sound waves in hydrogen gas corresponding to hydrogen at N.T.P. is 1/16th of air. Given that the speed of sound
the lower limit of audibility is (speed of sound in hydrogen gas is in air is 332 m/s.
about 1350 m/s)
67. If speed of sound wave is V0 at 0°C then find change in speed by
(a) 60 m (b) 67.5 m (c) 100 m (d) 500 m increasing temperature by t °C.

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 68. IF temperature increases by 3°C then speed of sound increased Intensity of Wave
by?
69. Temperature at which the speed of sound in air becomes doubled
77. If amplitude becomes half and frequency becomes one-fourth then
its value at 0°C is-
intensity of wave becomes-
(a) 1092°C (b) 819°C
78. A sound wave y = A sin (wt – kx) is propagating through a medium
(c) 819K (d) 546°C
of density r. What is the sound energy per unit volume?
70. What is the phase difference between the displacement wave and
1 2 2
pressure wave in sound wave? (a) rA w (b) rA2w2
2
(a) Zero (b) p/2 (c) p (d) p/4
(c) 2 rA2w2 (d) 4 rA2w2
71. Stationary point source emits sound uniformly in all directions in
79. As a wave propagates-
non-absorbing medium two points P and Q are at a distance of
4 m and 9 m respectively from the source. The ratio of amplitudes A. The wave intensity remains constant for a plane wave.
of the waves at P and Q is- B. The wave intensity decreases as the inverse of the distance
from the source for a spherical wave.
(a) 3/2 (b) 4/9 (c) 2/3 (d) 9/4
C. The wave intensity decreases as the inverse square of the
72. A big explosion on the moon cannot be heard on the earth because-
distance from the source for a spherical wave.
(a) The explosion produces high frequency sound waves which D. Total intensity of the spherical wave over the spherical
are inaudible. surface centered at the source remains constant at all times.
(b) Sound waves require a material medium for propagation. (a) 1, 2 (b) 1, 3
(c) Sound waves are absorbed in the moon's atmosphere. (c) 1, 2, 4 (d) 1, 3, 4
(d) Sound waves are absorbed in the earth's atmosphere. 80. A line source emits a cylindrical expanding wave. If the medium
73. The speed of sound in a medium depends on- absorbs no energy then the amplitude will vary with distance r
(a) The elastic property but not on the inertia property. from the source as proportional to-
(b) The inertia property but not on the elastic property. (a) r–1 (b) r–2 (c) r–1/2 (d) r1/2
(c) The elastic property as well as the inertia property 81. If the pressure amplitude in a sound wave is tripled, then by what
(d) Neither the elastic property nor the inertia property. factor the intensity of sound wave is increased?
74. The velocity of sound in air is affected by change in the- (a) 3 (b) 6 (c) 9 (d) 3
A. Atmospheric pressure 82. If the intensity of sound is doubled, the intensity level will increase
B. Moisture content of air by nearly-
C. Temperature of air (a) 1 dB (b) 2dB (c) 3 dB (d) 4 dB
D. Composition of air
(a) (i), (ii), (iii) (b) (i), (ii), (iv)
(c) (ii), (iii), (iv) (d) (ii), (iii) Loudness of Sound Wave
75. Velocity of sound in air-
A. Increases with temperature 83. What is the intensity of sound of 70 decibel? (Given the reference
B. Decreases with temperature intensity I0 = 10–12 watt/m2).
C. Increase with pressure 84. If the intensity of sound is increased by a factor of 30, by how
D. Is independent of pressure many decibels is the sound level increased?
Choose the correct answer. (a) 12 dB (b) 14.77 dB
(a) 1 and 2 (b) 1 and 3 (c) 10 dB (d) 13 dB
(c) 2 and 3 (d) 1 and 4 85. The sound intensity level at a point 4 m from the point source is 10
76. Given below are two statements: One is labelled as Assertion (A) dB, then the sound level at a distance 2 m from the same source
and the other is labelled as Reason (R). will be-
Assertion (A): Sound travels faster on a rainy day than on a dry
(a) 26 dB (b) 16 dB
day. (c) 23 dB (d) 3 dB
Reason (R): Moisture increases the pressure.
86. A sound absorber attenuates the sound level by 20 dB. TV intensity
In the light of the above statements, choose the most appropriate decreases by a factor of-
answer from the options given below: (a) 100 (b) 1000
(a) Both (A) and (R) are true and (R) is the correct explanation (c) 10000 (d) 10
of (A). 87. A person speaking normally produces a sound intensity of 40
(b) Both (A) and (R) are true and (R) is Not the correct dB at a distance of 1 m. If the threshold intensity for reasonable
explanation of (A). audibility is 20 dB, the maximum distance at which he can be hear
(c) (A) is true but (R) is false. clearly is-
(d) (A) is false but (R) is true. (a) 4 m (b) 5 m (c) 10 m (d) 20 m

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2024 - Question Bank 5
 Superposition of Waves 100. The equations of two waves are given by-

y1 = 5 sin 2p(x – vt) cm
88. If y = 6 sin (kx – wt), y2 = 4 sin (kx – wt) then find net intensity and
y2 = 3 sin 2p(x – vt + 1.5) cm
amplitude. These waves are simultaneously passing through a string. The
amplitude of the resulting wave is-
π
89. If y1 = 4 sin (wt – kx), y2 = 4 sin (kx – wt –
) resultant amplitude. (a) 2 cm (b) 4 cm (c) 5.8 cm (d) 8 cm
3
90. Two waves represented by y = a sin (wt – kx) and y = a sin 101. In a hall, a person receives direct sound waves from a source 120m
2π away. He also receives waves from the same source which reach
(wt – kx + ) are superposed. What will be the amplitude of the
3 him after being reflected from the 25m high ceiling at a point
resultant wave? halfway between them. The two waves interfere constructively
91. Two waves represented by y1 = 3 sin (200x – 150t) and y2 = 3 cos for wavelengths (in metres).
(200x – 150t) are superposed where x and y are in metre and t is in 10 10 20 20
(a) 10, m (b) 20, m
second. Calculate the amplitude of resultant wave. 2 3 3 5
92. On the superposition of the two waves given as y1 = A0 sin
(c) 30, 20, 10 (d) 35, 25, 15
π
(wt – kx) and y2 = A0 cos (wt + kx + ), the resultant amplitude 102. Two sources of sound are placed along the diameter of a circle of
6
of oscillations will be- radius R(R >> 4l). How many minima will be heard as one moves
(a) 3 A0 (b) A0/2 along the perimeter of circle.

3
(c) A0 (d) A
2 0
 R
93. Two waves of amplitudes A0 and xA0 pass through a region. If
x > 1, the difference in the maximum and minimum resultant S2 S1
amplitude possible is-
(a) (x + 1) > A0 (b) (x – 1) A0
4
(c) 2x A0 (d) 2A0
94. Two periodic waves of intensities I1 and I2 pass through a region
at the same time in the same direction. The sum of the maximum
and minimum intensities is- (a) 12 (b) 16 (c) 4 (d) 20
(a) 2(I1 + I2) (b) I1 + I2

Reflection, Refraction of Wave

( )
2
( )
2
(c) I1 + I 2 (d) I1 − I 2
95. Two waves have equations x1 = a sin (wt + f1) x2 = a sin 103. When sound wave is refracted from air to water, which of the
(wt + f2). If in the resultant wave the frequency and amplitude following will remain unchanged?
remain equal to amplitude of superimposing waves, the phase
(a) Wave number (b) Wavelength
difference between them is-
(c) Wave velocity (d) Frequency
π 2π π π
(a) (b) (c) (d) 104. The sound waves of frequency 660 Hz fall normally on a
6 3 4 3 perfectly reflecting wall. The shortest distance from the wall at
96. Two sound waves, each of amplitude A and frequency w superpose which the air particles have maximum amplitude of vibration is
π (v = 330 m/s).
at a point with phase difference of . The amplitude and frequency
2 (a) 0.5 m (b) 0.25 m (c) 0.125 m (d) 1 m
of the resultant wave are respectively.
A ω A ω (d)
(a) , (b) ,ω (c) 2 A, 2 A, ω
2 2 2 2 Stationary Wave
97. The ratio of intensities between two coherent sound source is 4 :
1. The difference of loudness in decibels (dB) between maximum
105. A stationary wave is represented by y = A sin(100t) cos(0.01x),
and minimum intensities, when they interfere in space is-
where y and A are in millimetres, t is in second and x is in metre.
(a) 10 log 2 (b) 20 log 3 The velocity of the constituent wave is-
(c) 10 log 3 (d) 20 log 2 (a) 104 m/s (b) Not derivable
I1 9
98. If = then find I max = ? (c) 1 m/s (d) 102 m/s
I2 4 I min 106. The equation given below represents a stationary wave set-up in a
medium y = 12 sin(4pX) sin(40 pt), where y and x are in cm and t
I max 25 I
99. = then find 1 = ? is in second. Calculate the amplitude, wavelength and velocity of
I min 16 I2 the component waves.

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6 Class Question Bank
107. A wave y = a sin (wt – kx) on a string meets with another wave 118. A wire of length one metre under a certain initial tension emits
producing a node at x = 0. Then the equation of the unknown a sound of fundamental frequency 256 Hz. When the tension is
wave is- increased by 1 kg wt, the frequency of the fundamental mode
increases to 320 Hz. The initial tension is-
(a) y = a sin (wt – kx) (b) y = – a sin (wt – kx)
(c) y = a cos (wt – kx) (d) y = –a cos (wt – kx) (a) 3/4 kg wt (b) 4/3 kg wt
(c) 16/9 kg wt (d) 20/9 kg wt
108. In a stationary wave, what is the amplitude of oscillation for a
particle located between a node and an antinode? Additionally, 119. A string is stretched between fixed points separated by 75.0 cm. It
what is the frequency of oscillation for that particle? is observed to have resonant frequencies of 420 Hz and 315 Hz.
There are no other resonant frequencies between these two. The
109. The constituent waves of a stationary wave have amplitude, lowest resonant frequency for this string is-
frequency and velocity as 8 cm, 25 Hz and 150 cm s–1 respectively.
(a) 10.5 Hz (b) 105 Hz (c) 155 Hz (d) 205 Hz
What is the amplitude of the stationary wave at x = 2 cm.
120. A standing wave having 3 nodes and 2 antinodes is formed
110. In a standing wave, all particles of the medium cross the mean between two atoms having a distance 1.21 Å between them. The
position with- wavelength of the standing wave is-
(a) Different speeds at different instants (a) 6.05 Å (b) 242 Å (c) 1.21 Å (d) 3.63 Å
(b) Different speeds at same instant 121. A wave disturbance in a medium is described by
(c) Same speed at different instants y(x, t) = 0.02 cos (50 pt + p/2) cos (10 px),
(d) Same speed at same instant Where x and y are in metres and t in seconds.
111. In a stationary wave pattern, all the particles- A. A node occurs at x = 0.15 m
A. Of the medium vibrate in the same phase. B. An antinode occurs at x = 0.3 m
B. In the region between two antinodes vibrate in the same C. The speed of the wave is 5.0 m/s
phase. D. The wavelength is 0.2 m
C. In the region between two succesive nodes vibrate in the (a) A, C, D (b) B, C, D
same phase. (c) A, B, C, D (d) C, D
D. On either side of a node vibrate in opposite phase. 122. Standing waves are produced in 10m long stretched string. If the
Choose the correct statement: string vibrates in 5 segments and wave velocity is 20 m/s, the
frequency is-
(a) 1, 3, 4 (b) 1, 2, 3, 4 (c) 3, 4 (d) 1, 2, 3
(a) 5 Hz (b) 10 Hz (c) 2 Hz (d) 4 Hz
123. A string is cut into three parts, having fundamental frequencies n1,
n2, n3 respectively. Then original fundamental frequency n related
Stationary Wave in a String by the expression as-
1 1 1 1
(a) = + + (b) n = n1 × n2 × n3
112. A string 50 cm long is under a tension of 20 N force. Calculate the n n1 n2 n3
frequency of fundamental mode given that mass of the string is 1g. n1 + n2 + n3
(c) n = n1 + n2 + n3 (d) n =
113. The tension in a wire is decreased by 19%. The percentage 3
124. A stretched string resonants with tuning fork frequency 512
decrease in frequency will be-
Hz when length of the string is 0.5 m. The length of the string
(a) 0.19% (b) 10% (c) 19% (d) 0.9% required to vibrate resonantly with a tuning fork of frequency 256
114. The string of a violin has a frequency of 440 cps. If the violin Hz would be-
string is shortened by one fifth, its frequency will be changed to- (a) 0.25 m (b) 0.5 m (c) 1 m (d) 2 m
(a) 440 cps (b) 880 cps 125. A uniform string resonates with a tuning fork, at a maximum
(c) 550 cps (d) 2200 cps tension of 32 N. If it is divided into two segments by placing a
wedge at a distance one-fourth of length from one end, then to
115. The string of a violin has a frequency of 440 cps. If the violin
resonance with same frequency the maximum value of tension for
string is shortened to one fifth, its frequency will be changed to-
string will be
(a) 440 cps (b) 880 cps
(a) 2 N (b) 4 N (c) 8 N (d) 16 N
(c) 550 cps (d) 2200 cps
126. The tension in a stretched string fixed at both ends is changed by
116. A 12 m long vibrating string has the speed of wave 48 m/s. To what 2%, the fundamental frequency is found to get changed by 15 Hz.
frequency it will resonate? A. Wavelength of the string of fundamental frequency does not
(a) 2 cps (b) 4 cps change
(c) 6 cps (d) All of these B. Velocity of propagation of wave changes by 2%
117. A certain string will resonate to several frequencies, the lowest of C. Velocity of propagation of wave changes by 1%
which is 200 cps. What are the next three higher frequencies to D. Original frequency is 1500 Hz
which it resonates? Choose the correct statements(s)–
(a) 400, 600, 800 (b) 300, 400, 500 (a) 1, 2, 3, 4 (b) 1, 2, 4
(c) 100, 150, 200 (d) 200, 250, 300 (c) 1, 3, 4 (d) 1, 2, 3

MR PHYSICS for questions practice

2024 - Question Bank 7
127. A string 2.0 m long and fixed at its end is driven by a 240 Hz 137. In case of closed pipe which harmonic the pth overtone will be-
vibrator. The string vibrates in its third harmonic mode. The speed (a) 2p + 1 (b) 2p – 1 (c) p + 1 (d) p – 1
of the wave and its fundamental frequency is-
138. A closed pipe of length 10 cm has its fundamental frequency half
(a) 320 m/s, 120 Hz (b) 180 m/s, 80 Hz that of the second overtone of an open pipe. The length of the open
(c) 180 m/s, 120 Hz (d) 320 m/s, 80 Hz pipe.
128. A string is clamped at both the ends and it is vibrating in its 4th (a) 10 cm (b) 20 cm (c) 30 cm (d) 40 cm
harmonic. The equation of the stationary wave is Y = 0.3 sin
139. The vibrations of four air columns under identical conditions
(0.157x) cos(200pt). The length of the string is: (All quantities are
are represented in the figure below. The ratio of frequencies
in SI units.)
np : nq : nr : ns will be-
(a) 20 m (b) 80 m (c) 60 m (d) 40 m
129. A wire of length L and mass per unit length 6.0 × 10–3 kg m–1 is
put under tension of 540 N. Two consecutive frequencies that it
resonates at are 420 Hz and 490 Hz. Then L in meters is-
(a) 1.1 m (b) 5.1 m (c) 2.1 m (d) 8.1 m

p q r s
Sonometer Wire (a) 12 : 6 : 3 : 4 (b) 1 : 2 : 4 : 3
(c) 4 : 2 : 3 : 1 (d) 6 : 2 : 3 : 4
130. A sonometer wire is under a tension of 10 N and the length between 140. A closed organ pipe (closed at one end) is excited to support the
the bridges is 2m. A metre long wire of sonometer has mass of third overtone. It is found that air in the pipe has-
1.0 gm. Deduce the speed of transverse wave and the frequency (a) Three nodes and three antinodes
of 1st harmonic.
(b) Three nodes and four antinodes
131. The length of a sonometer wire is 0.75 m and density 9 × 103 kg/
(c) Four nodes and three antinodes
m3. It can bear a stress of 8.1 × 108 N/m2 without exceeding the
elastic limit. The fundamental frequency that can be produced in (d) Four nodes and four antinodes.
the wire, is- 141. For a particular resonance tube, following are four of the six
(a) 200 Hz (b) 150 Hz (c) 600 Hz (d) 450 Hz harmonics below 1000 Hz;
132. If the tension and diameter of a sonometer wire of fundamental 300, 600, 750 and 900 Hz
frequency n is doubled and density is halved then its fundamental The two missing harmonics are-
frequency will become- (a) 75, 150 (b) 150, 450 (c) 400, 800 (d) 250, 400
n n 142. The fundamental frequency of a closed organ pipe of length 20 cm
(a) (b) 2n (c) n (d)
2 2 is equal to the second overtone of an organ pipe open at both the
133. The length of a sonometer wire AB is 110 cm. Where should the ends. The length of organ pipe open at both the ends is-
two bridges be placed from A to divide the wire in 3 segments (a) 140 cm (b) 80 cm (c) 100 cm (d) 120 cm
whose fundamental frequencies are in the ratio of 1 : 2 : 3 ?
143. For a certain organ pipe, three successive resonance frequencies
(a) 60 cm and 90 cm (b) 30 cm and 60 cm are observed at 425, 595, and 765 Hz respectively. Taking the
(c) 30 cm and 90 cm (d) 40 cm and 80 cm speed of sound in air to be 340 m/s the fundamental frequency of
134. The length of the wire between two ends of a sonometer is 100 cm. the pipe (in Hz) is-
What should be the positions of two bridges below the wire so that (a) 425 (b) 170 (c) 85 (d) 245
the three segments of the wire have their fundamental frequencies 144. In a closed organ pipe of length 105 cm, standing waves are set up
in the ratio 1 : 3 : 5.
corresponding to third overtone. What distance from the closed
1500 500 1500 300 end, a pressure node is formed?
(a) cm, cm (b) cm, cm
23 23 23 23 (a) 5 cm (b) 15 cm (c) 25 cm (d) 30 cm
300 1500 1500 200 145. A second harmonic has to be generated in a string of length ℓ
(c) cm, cm (d) cm, cm
23 23 23 23 stretched between two rigid supports. The points where the string
has to be plucked and touched are respectively.
   3    3
Open and Close Organ Pipe (a) ,
4 2
(b)
4
,
4
(c) ,
2 2
(d)
2
,
4
146. The two nearest harmonics of a tube closed at one end and open
135. If 7th overtone is 120 Hz then find fundamental frequency of open at other end are 220 Hz and 260 Hz. What is the fundamental
organ pipe. frequency of the system?
136. A cylindrical tube, open at both ends, has a fundamental frequency (a) 10 Hz (b) 20 Hz (c) 30 Hz (d) 40 Hz
f in air. The tube is dipped vertically in water so that half of it is in 147. The number of possible natural oscillations of air column in a pipe
water. The fundamental frequency of the air column is now. closed at one end of length 85 cm whose frequencies lie below
f 3f 1250 Hz are (velocity of sound = 340 ms–1)
(a) (b) (c) f (d) 2f
2 4 (a) 4 (b) 5 (c) 7 (d) 6

MR PHYSICS for questions practice

8 Class Question Bank
148. The second overtone of an open organ pipe has the same frequency 158. Two vibrating tuning forks produce progressive waves given by y1
as the first overtone of a closed pipe L metre long. The length of = 4 sin 500pt and y2 = 2sin506pt. Number of beats produced per
the open pipe wil be- minute is-
(a) L (b) 2L (c) L/2 (d) 4L (a) 360 (b) 180 (c) 3 (d) 60
149. An air column, closed at one end and open at the other, resonates 159. Two source of sound placed close to each other, are emitting
with a tuning fork when the smallest length of the column is 50cm. progressive waves given by y1 = 4 sin 600pt and y2 = 5 sin (608pt).
The next larger length of the column resonating with the same An observer located near these two source of sound will hear-
tuning fork is- (a) 8 beats per second with intensity ratio 81 : 1 between waxing
and waning.
(a) 200 cm (b) 66.7 cm (c) 100 cm (d) 150 cm
(b) 4 beats per second with intensity ratio 81 : 1 between waxing
150. If we study the vibration of a pipe open at both ends, then the
and waning.
following statement is not true:
(c) 4 beats per second with intensity ratio 25 : 16 between waxing
(a) Odd harmonics of the fundamental frequency will be and waning.
generated. (d) 8 beats per second with intensity ratio 25 : 16 between waxing
(b) All harmonics of the fundamental frequency will be and waning.
generated. 160. A source of unknown frequency gives 4 beats/s, when sounded
(c) Pressure change will be maximum at both ends. with a source of known frequency 250 Hz. The second harmonic
(d) Open end will be antinode. of the source of unknown frequency gives five beats per second,
when sounded with a source of frequency 513 Hz. The unknown
151. The fundamental frequency of a vibrating organ pipe is 200 Hz. frequency is-
A. The first overtone is 400 Hz. (a) 246 Hz (b) 240 Hz (c) 260 Hz (d) 254 Hz
B. The first overtone may be 400 Hz. 161. The string of a violin emits a note of 205 Hz at its correct tension.
C. The first overtone may be 600 Hz. the string is tightened slightly and then it produces six beats in two
D. 600 Hz is an overtone. second with a tuning fork of frequency 205 Hz. The frequency of
the note emitted by the taut string is-
(a) 1, 4 (b) 1, 2, 3 (c) 3, 4 (d) 2, 3, 4
(a) 211 Hz (b) 199 Hz (c) 208 Hz (d) 202 Hz
152. The fundamental frequency of a closed organ pipe is equal to the
first overtone frequency of an open organ pipe. If length of the 162. A source of frequency v gives 5 beats/second when sounded with
a source of frequency 200 Hz. The second harmonic of frequency
open pipe is 60 cm, the length of the closed pipe will be-
2v of source gives 10 beats/second when sounded with a source of
(a) 60 cm (b) 45 cm (c) 30 cm (d) 15 cm frequency 420 Hz. The value of v is-
153. A closed and an open organ pipe have same lengths. If the ratio of (a) 205 Hz (b) 195 Hz (c) 200 Hz (d) 210 Hz
 a −1 163. When two tuning forks (fork 1 and fork 2) are sounded together,
frequencies of their seventh overtones is   then the value
of a is __________.  a  4 beats per second are heard. Now some tape is attached on the
prong of the fork 2. When the tuning forks are sounded again, 6
154. A tuning fork of frequency 480 Hz is used in an experiment for beats per second are heard. If the frequency of fork 1 is 200 Hz,
measuring speed of sound (V) in air by resonance tube method. then what was the original frequency of fork 2?
Resonance is observed to occur at two successive lengths of the
air column,  1 = 30 cm and  2 = 70 cm. Then V is equal to- (a) 204 Hz (b) 196 Hz (c) 202 Hz (d) 200 Hz
(a) 332 ms–1 (b) 338 ms–1 (c) 384 ms–1 (d) 397 ms–1 164. A tuning fork of unknown frequency produces 4 beats per second
when sounded with another tuning fork of frequency 254 Hz. It
155. A closed organ pipe has a fundamental frequency of 1.5 kHz.
gives the same number of beats per second when unknown tuning
The number of overtones that can be distinctly heard by a person
fork loaded with wax. The unknown frequency before loading
with this organ pipe will be: (Assume that the highest frequency a with wax is-
person can hear is 20,000 Hz)
(a) 258 (b) 254
(a) 6 (b) 4 (c) 7 (d) 5
(c) 250 (d) Can't be determined
165. Ten tuning forks are arranged in increased order of frequency in
such a way that any two consecutive tuning forks produce 4 beats
Beats per second. The highest frequency is twice that of the lowest.
Possible highest and lowest frequencies (in Hz) are-
156. A tuning fork and an air column whose temperature is 51oC (a) 80 and 40 (b) 100 and 50
produce 4 beats in one second, when sounded together. When (c) 44 and 22 (d) 72 and 36
the temperature of air column decreases the number of beats per 166. Two tuning fork A and B are sounded together gives 5 beats per
second decreases. When the temperature remains 16°C only one second. If frequency of B is 260 Hz and after loading B with wax
beat per second is produced. The frequency of the tuning fork is- the beat frequency increase the frequency of A is-
(a) 100 Hz (b) 75 Hz (c) 150 Hz (d) 50 Hz (a) 265 Hz (b) 255 Hz (c) 260 Hz (d) 250 Hz
157. A tuning fork resonates with a sonometer wire of length 1 m 167. A tuning fork A of unknown frequency produces 5 beats/s with a
stretched with a tension of 6 N. When the tension in the wire fork of known frequency 340 Hz. When fork A is filed, the beat
frequency decreases to 2 beats/s. What is the frequency of fork A?
is changed to 54 N, the same tuning fork produces 12 beats per
second with it. The frequency of the tuning fork is______ Hz. (a) 345 Hz (b) 338 Hz (c) 342 Hz (d) 335 Hz

MR PHYSICS for questions practice

2024 - Question Bank 9
 MR* CORNER

1. Statement I: A sine wave is Travelling in a medium The minimum Statement II: Two periodic waves of amplitudes A1 and A2 pass

distance Between The Two particles, always having same speed is through a region. If A1 > A2, the difference in maximum and
equal to the wavelength of the wave. minimum resultant amplitude possible will be equal to two times
Statement II: A sine wave is Travelling in medium. A particular
the amplitude of second wave (A2).
Particle has zero. Displacement at a certain instant The particle 5. Statement I: A Sonometer wire of length l vibrates in fundamental
closest to it having zero displacement is at distance half of the mode when excited by a tuning fork of frequency 416 Hz. If the
length is doubled keeping other quantities same, the string will
wavelength of wave.
vibrate with frequency of 208 Hz
2. Statement I: The equation y = A sin2 (kx - wt) represents a motion
A w Statement II: Two particles A and B have phase difference p

with Amplitude and Frequency . when a sine wave passes through the region. A and B will move in
2 p
Statement II: X-Ray's are mechanical wave. opposite direction.
3. Statement I: A cork floating in a calm pond executes SHM with 6. Statement I: A Mechanical wave propagates in a medium along
frequency v when a wave generated by a boat passes by it, The the X-axis. The particles of the medium must move on the Y axis
v or Z axis.
frequency of wave generated will be .
2 Statement II: A Transverse wave travels along Z axis. The particle

Statement II: Two strings A and B, made of same material are of medium must move in X-Y Plane.
stretched by same Tension, the radius of string A is double of the
7. Statement I: A Wave going in a solid must be transverse.
radius of B. A transverse wave travels on A with speed VA and on
VB Statement II: A wave moving in a gas must be longitudinal.

B with speed VB. The ratio will be equal to 4.
VA 8. Statement I: A standing wave is produced on a string clamped at
4. Statement I: A wave pulse, travelling on two-piece string, gets one end and free at the other. The length of the string must be an
partially reflected and partially transmitted at the junction. The l
reflected wave is inverted in shape as compared to the incident integral multiple of .
4
wave. The wavelength of transmitted wave will be lesser in value Statement II: In a stationary wave, all the antinodes vibrate in
as compared to wavelength of reflected wave and incident wave. same phase.

MR PHYSICS for questions practice

10 Class Question Bank
 Answer Key

1. (c) 2. (d) 3. (a) 4. (d) 5. 2 m 6. (a) 7. (c) 8. (d) 9. (b) 10. (b)

11. (d) 12. (a) 13. (a) 14. (c) 15. (b) 16. (b) 17. 12 m/s 18. (d) 19. (c) 20. (c)

21. (c) 22. (a) 23. (c) 24. (a) 25. (a) 26. (a) 27. (b) 28. (a) 29. (d) 30. (a)

31. (a) 32. (c) 33. (c) 34. (a) 35. (a) 36. (d) 37. (d) 38. (c) 39. (a)

40. 100m/s 41. (c) 42. (a) 43. 200 m/s 44. (c) 45. (d) 46. (c) 47. (a) 48. (b) 49. (a)

50. 2% 51. Speed will not change 52. Speed of sound become double 53. 5000 m/s 54. 196 × 107 N/m2 55. (b)

56. 8.5 ×102 kg/m3 57. (b) 58. (c) 59. 15% 60. (a) 61. (a) 62. (b) 63. 900 K 64. (c)

65. Remain same 66. 1328 m/s 67. 0.61t oC 68. 1.83 m/s 69. (b) 70. (b) 71. (d) 72. (b)

73. (c) 74. (c) 75. (d) 76. (c) 77. Decrease by 64 time 78. (a) 79. (d) 80. (c) 81. (c)

82. (c) 83. 10–5 w/m2 84. (b) 85. (b) 86. (a) 87. (c) 88. Anet = 10, Inet = 100 89. 4√3

90. Anet = a 91. Amplitude of resultant wave =3√2 m. 92. (c) 93. (d) 94. (a) 95. (b) 96. (d) 97. (b)

98. 25/1 99. 81/1 100. (a) 101. (a) 102. (a) 103. (d) 104. (c) 105. (a) 106. l = 0.5 m, v = 10m/s

ω
107. (b) =
108. A 2 A, f
= 109. 8 3cm 110. (b) 111. (c) 112. 100 113. (b) 114. (c) 115. (d)
2π
116. (d) 117. (a) 118. (c) 119. (b) 120. (c) 121. (c) 122. (a) 123. (a) 124. (c) 125. (a)

126. (c) 127. (d) 128. (b) 129. (c) 130. 100 m/s 131. (a) 132. (c) 133. (a) 134. (a)

135. 15 Hz 136. (c) 137. (a) 138. (c) 139. (b) 140. (d) 141. (b) 142. (d) 143. (c) 144. (b)

145. (a) 146. (b) 147. (d) 148. (b) 149. (d) 150. (c) 151. (d) 152. (d) 153. 6 154. (c)

155. (c) 156. (d) 157. 6 158. (b) 159. (b) 160. (d) 161. (c) 162. (a) 163. (b) 164. (a)

165. (d) 166. (a) 167. (d)

MR* CORNER

1. I. False, II. True 2. I. True, II. False 3. Both are false 4. Both are True 5. I. False, II. True
6. I. False, II. True 7. I. False, II. True 8. I. True, II. False

MR PHYSICS for questions practice

2024 - Question Bank 11