1

PHYSICS
WAVE MOTION WAVE MOTION

nLEVEL -I o
EXERCISE - I
Wave Equations & Basics :
1. Which of the following expressions represents a simple harmonic progressive wave
1) y = A sin wt 2) y = A sin wt cos kx
3) y = A sin (wt-kx) 4) y = A cos kx
 
2. The displacement y of a particle in a medium can be expressed as y = 10–6 sin  100 t  20 x  m
 4
where 't' is in second and x in metre. The speed of wave is
1) 2000 ms–1 2) 5 ms–1 3) 20 ms–1 4) 5  ms–1

3. The equation of a transverse wave travelling on a rope is given by y  10 sin   0.01x  2.00 t  where
y and x are in cm and t in seconds. The maximum transverse speed of a particle in the rope is about
1) 62.8 cm/s 2) 75 cm/s 3) 100 cm/s 4) 121 cm/s
4. The angular frequency of a particle in a progressive wave in an elastic medium is 100  rads-1 and it is
moving with a velocity of200ms-1. The phase difference between two particles seperated by a distance
of 20m is
3
1) 31.4 rad 2)  rad 3) rad 4) 36 rad
4
5. A progressive wave moves with a velocity of 36m/s in a medium with a frequency of 200Hz. The
phase difference between two particles seperated by a distance of 1cm is
 0
1) 40° 2) 20 rad 3) rad 4)
9 9
6. The speed of a wave in a medium is 760 m/s. If 3600 waves are passing through a point in the medium
in 2 minutes, then its wavelength is
1) 13.8 m 2) 25.3 m 3) 41.5 m 4) 57.2 m
7. A progressive wave of frequency 500 Hz is travelling with a speed of 350 m/s. A compressional
maximum appears at a place at a given instant. The minimum time interval after which of refraction
maximum occurs at the same place is
1 1 1 1
1) s 2) s 3) s 4) s
250 500 1000 350
8. A wave of length 2m is superposed on its reflected wave to form a stationary wave. A node is located
at x = 3m. The next node will be located at x =
1) 3.25 m 2) 3.50 m 3) 3.75 m 4) 4m
 x 
9. The equation of a stationary wave is y= 0.8cos   sin(200  t) where x is in cm and t is in seconds.
 20 
The separation between consecutive nodes is
1) 10 cm 2) 20 cm 3) 30 cm 4) 40 cm
Strings :
10. Length of a string tied to two rigid supports is 40 cm. Maximum wavelength in cm of a stationary wave
produced on it is (AIEEE 2002)
1) 20 cm 2) 80 cm 3) 40 cm 4) 120 cm
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11. The length of a sonometer wire AB is 100 cm, where should the two bridges be placed from A to divide
the wire in 3 segments whose fundamental frequencies are in the ratio of 1 : 2 : 6
1) 30 cm, 90 cm 2) 60cm, 90 cm 3) 40 cm, 80 cm 4) 20 cm, 30 cm
12. A 5.5 m long string has a mass of 0.035 kg. If the tension in the string is 77 N, the speed of a wave on
the string is
1) 110 m/s 2) 165 m/s 3) 77 m/s 4) 102 m/s
13. The length of a sonometer wire tuned to a frequency of 256 Hz is 0.6 m. Calculate the frequency of the
tuning fork with which the vibrating wire will be in tune when the length is made 0.4 m.
1) 78 Hz 2) 512 Hz 3) 384 Hz 4) 126 Hz
14. The fundamental frequency of a string stretched with a weight of 4kg is 256 Hz. The weight required to
produce its octave is
1) 4 kg wt 2) 12 kg wt 3) 16 kg wt 4) 24 kg wt
15. Two strings A and B, made of the same material, have equal lengths. The cross sectional area of A is
half that of B while the tension on A is twice that on B. The ratio of the velocities of transverse waves
in A and B is
1) 2:1 2) 1: 2 3) 2 : 1 4) 1 : 2
16. The density of the stretched string is changed by 2% without change in tension and radius. The change
in transverse wave velocity.
1) 2% increase 2) 1% increase 3) 1% increase or decrease 4) 4% change
17. The tension in the string is changed by 2% what is the change in the transverse wave velocity
1) 1% 2) 2% 3) 3% 4) 4%
18. To increase the frequency by 20 % ,the tension in the string vibrating on a sonometer has to be increased by
1) 44 % 2) 33% 3) 22 % 4) 11% (2007 M)
19. When the tension in a string is increased by 44%. the frequency increased by 10Hz the frequency of the
string is
1) 100 Hz 2) 200 Hz 3) 150 Hz 4) 50 Hz
-3
20. A wire whose linear density is 5 x 10 kg/m is stretched between two points with a tension 450 N. The
wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates
is 490 Hz. What is the length of the wire?
1) 1.2 m 2) 1.8 m 3) 2.1 m 4) 8.1 m
21. In order to double the frequency of the fundamental note emitted by a stretched string, the length is
reduced 3/4 th of the original length and the tension is changed. The factor by which the tension is to
be changed is (2001 E)
3 2 8 9
1) 2) 3) 4)
8 3 9 4
22. Two uniform strings 'A' and 'B' made of steel are made to vibrate under the same tension. If the first
overtone of 'A' is equal to the second overtone of 'B' and if the radius of 'A' is twice that of 'B' the ratio
of the lengths of the string is (2003 E)
1) 1:2 2) 1:3 3) 1:4 4) 1:5
23. Transverse waves are generated in two steel wires A and B by attaching their free ends to a vibrating
source of frequency 500 Hz. The diameter of A is half that of B and tension on B is double that on A.
What is the ratio of the velocities of waves in wires A and B?
1) 1 : 2 2) 2 : 1 3) 1 : 2 4) 2 : 1

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24. The third overtone produced by a vibrating string 0.5m long is 1200Hz. The speed of propagation of
1
the wave in ms is
1) 400 2) 300 3) 600 4) 1200
25. A wave of frequency 100Hz is sent along a string towards a fixed end. When this wave travles back
then after reflection, a node is formed at a minimum distance of 10 cm from the fixed end of the string.
The speed of the incident wave is
1) 40 m/s 2) 20 m/s 3) 10 m/s 4) 5 m/s
Velocity of Sound :
26. The temperature at which the speed of sound in air becomes double of its value at 00C is [AIEEE 2002]
1) 273 K 2) 546 K 3) 1092 K 4) 0 K
27. The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is [IIT 99]
1) 2 / 7 2) 1/ 7 3) 3 / 5 4) 6 / 5
28. The speed of sound in air at 150C and 76 cm of Hg is 340 m/s. The speed of sound in air at 300C and
75 cm of Hg will be (in m/s)
303 288 2  75
1) 340 2) 340 3) 340 2 4) 340
288 303 76
29. The velocities of sound in an ideal gas at temperature T1 and T2 K are found to be V1 and V2 respectively.
If the r.m.s velocities of the molecules of the same gas at the same temperatures T1 and T2 are  1 and
 2 respectively then
 V1   V2  V2 V1
1) 2  1  V  2) 2  1  V  3) 2  1 V 4) 2  1 V
2 1 1 2

30. 1 and 2 are the velocities of sound at the same temperature in two monoatomic gases of densities
1  1
1 and 2 respectively. If   4 then the ratio of velocities 1 and 2 is
2
1) 1 : 2 2) 4 : 1 3) 2 : 1 4) 1 : 4
Pipes :
31. An open organ pipe sounds a fundamental note of frequency 330 Hz. If the speed in air is 330 m/s then
the length of the pipe is nearly
1) 0.25 m 2) 0.50 m 3) 0.75 m 4) 2.00 m
32. A cylindrical tube, open at both ends, has a fundamental frequency f0 in air. The tube is dipped
vertically into water such that half of its length is inside water. The fundamental frequency of the air
column now is
1) 3f0 / 4 2) f0 3) f0 / 2 4) 2f0
33. An organ pipe P1 , closed at one end and vibrating in its first overtone, and another pipe P2 open at both
ends and vibrating in its third overtone, are in resonance with a given tuning fork . The ratio of the
length of P1 to that of P2 is
8 3 1 1
1) 2) 3) 4)
3 8 2 3
34. An open pipe 30 cm long and a closed pipe 23 cm long, both of the same diameter, are each sounding
their first overtone are in unison. The end correction of these pipes is
1) 0.5 cm 2) 0.3 cm 3) 1 cm 4) 1.2 cm
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35. Two closed organ pipes of length 100 cm and 101 cm produces 16 beats in 20 sec when each pipe is
sounded in its fundamental mode calculate the velocity of sound
1) 303 m/s 2) 332 m/s 3) 323.2 m/s 4) 300 m/s
36. If l1, l2 and l3are wave lengths of the waves giving resonance with fundamental, first and second over
tones of closed organ pipe. The ratio of wavelengths l1: l2:l3 is ..........
1 1
1) 1 : 2 : 3 2) 1 : : 3) 1 : 3 : 5 4) 5 : 3 : 1
3 5
37. An open organ pipe and closed pipe have same length. The ratio of frequencies of their nth over tone is ......
n 1 2( n  1) n n 1
1) 2) 3) 4)
2n  1 2n  1 2n  1 2n
38. Two pipes have each of length 2m. One is closed at one end and the other is open at both ends. The
speed of sound in air is 340m/s the frequency at which both can resonate is ............
1) 340 Hz 2) 510 Hz 3) 42.5 Hz 4) does not exist
39. The first overtone of an open pipe has frequency n. The first ovetone of a closed pipe of the same
length will have frequency
1) n/2 2) 2n 3) 3n/4 4) 4n/3
40. If a resonance tube is sounded with a tuning fork of frequency 256 Hz, resonance occurs at 35 cm and
105 cm. The velocity of sound is about
1) 360 m/s 2) 512 m/s 3) 524 m/s 4) 400 m/s
41. Fundamental frequency of pipe is 100 Hz and other two frequencies are 300 Hz and 500 Hz then
1) Pipe is open at both the ends 2) pipe is closed at both the ends
3) One end open and another end is closed 4) None of the above
Beats :
42. Two tuning forks when sounded together produce 5 beats in 2 seconds. The time interval between two
sucessive maximum intensities of sound is
1) 0.5 s 2) 0.2 s 3) 0.4 s 4) 0.3 s
43. Two progressive waves y1 = 4 sin 400  t and y2 = 3 Sin 404  t moving in the same direction superpose
on each other producing beats. Then the number of beats per second and the ratio of maxium to
minimum intensity of the resultant waves are respectively
5 49 16 49
1) 2 and 2) 4 and 3) 4 and 4) 2 and
1 1 9 1
44. Two sound waves of wavelengths 5 m and 6 m formed 30 beats in 3 seconds. The velocity of sound is
1) 300 ms-1 2) 310 ms-1 3) 320 ms-1 4) 330 ms -1
45. Two stretched wires of same length, diameter and same material are in unison. The tension in one is
increased by 2% and 2 beats per second are heard. What was the frequency of the note produced when
they were in unision
1) 100 Hz 2) 200 Hz 3) 300 Hz 4) 400 Hz
46. The frequency of a tuning fork A is 5% greater than that of a standard fork K. The frequency of another
fork B is 3% less than that of K. When A and B are vibrated simulataneously 4 beats per second are heard.
Find the frequencies of A and B.
1) 52.5 Hz, 48.5 Hz 2) 63.5 Hz, 79.5 Hz 3) 10.5 Hz, 101 Hz 4) 124 Hz, 120 Hz
47. 64 tuning forks are arranged such that each fork produces 4 beats per second with next one. If the
frequency of the last fork is octave of the first, the frequency of 16th fork is
1) 316 Hz 2) 322 Hz 3) 312 Hz 4) 308 Hz

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48. A tuning fork produces 4 beats per sec with one fork of frequency 288 cps. A little wax is placed on the
unknown fork and it produces 2 beats per second. The frequency of unknown fork is
1) 286 cps 2) 292 cps 3) 294 cps 4) 288 cps
49. A tuning fork produces 7 beats/s with a tuning fork of frequency 248Hz. Unknown fork is now loaded
and 7 beats/s are still heard. The frequency of unknown fork was
1) 241 Hz 2) 248 Hz 3) 255 Hz 4) 234 Hz
50. Tuning fork A of frequency 258 Hz gives 8 beats with a tuning fork B. When fork B is filed nd again
A and B are sounded the number of beats heard remains same. The frequency of B is
1) 250 Hz 2) 264 Hz 3) 258 Hz 4) 266 Hz
51. Two tuning forks A and B vibrating simultaneously produce 5 beats /s. Frequency of B is 512 Hz. If
one arm of A is filed, the number of beats per second increases. Frequency of A is
1) 502 Hz 2) 507 Hz 3) 517 Hz 4) 522 Hz
52. Tuning fork A of frequency 258 Hz gives 8 beats with a tuning fork B. When the tuning fork A is filed
and again A and B are sounded the number of beats heard decreases. The frequency of B is
1) 250 Hz 2) 266 Hz 3) 258 Hz 4) 242 Hz
53. Two tuning forks A and B vibrating simultaneously produce 5 beats /s. Frequency of B is 512 Hz. If
tuning fork B is now loaded with wax, when it vibrated with A the number of beats become 6 beats per
second. Frequency of A is
1) 502 Hz 2) 507 Hz 3) 517 Hz 4) 522 Hz
54. A tuning fork of frequency 340 Hz produces 5 beats per second with a sonometer wire. If the tension
is slightly increased the number of beats becomes 4. The frequency of sonometer wire is
1) 335 Hz 2) 345 Hz 3) 330 Hz 4) 350 Hz
55. Two tuning forks x and y produce tones of frequencies 256 Hz and 262 Hz respectively. An unknown
tone sounded with x produces, beats. When it is sounded with y the number of beats produced is
doubled. The unknown frequency is
1) 254 Hz 2) 258 Hz 3) 264 Hz 4) 259 Hz
56. A source of frequency ‘X’ gives 5 beats/s when sounded with a source of frequency 200 Hz. The
second harmonic of source gives 10 beats/s when sounded with a source of frequency 420 Hz. The
value of ‘x’ is
1) 200 Hz 2) 210 Hz 3) 205 Hz 4) 195 Hz
Echoes :
57. The minimum distance between the man and the reflecting surface so that he can hear the echo is
(velocity of sound 340 ms-1)
1) 16.5 m 2) 17m 3) 18m 4) 16 m
58. A man standing at some distance from a cliff hears the echo of sound after 2s. He walks 495 m away
from the cliff. He produces a sound there and recieves the echo after 5s. What is the speed of sound?
1) 330 m/s 2) 340 m/s 3) 390 m/s 4) 380 m/s
59. A person moving in a car with a velocity of 36 kmph towards a large wall blows a horn. If he hears the
echo after 3s, the distance of wall from him when he blows the horn (velocity of sound 340 ms-1)
1) 340 m 2) 1050m 3) 700m 4) 525 m
60. The height of a cloud above the earth is 100 m. If an observer hears the sound of a thunder 0.3s after
the lightening is seen, what is the velocity of sound on that rainy day
1) 300 m/s 2) 333.3 m/s 3) 100 m/s 4) 666.6 m/s

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61. A rifle is fired in a valley formed between two parallel mountains. The echo from one mountain is heard after
1.5s and from the other is heard 3s later. What is the width of the valley? (velocity of sound = 340 ms-1)
1) 1080 m 2) 1060 m 3) 1040 m 4) 1020 m
62. A man standing between two parallel cliffs produces sound and heard the first echo after 4 secs and next
echo after 2 sec later v = 330 ms-1. when is the third echo heard
1) 4s 2) 5 s 3) 10s 4) 6 s
Doppler Effect :
63. A whistle producing sound waves of frequencies 9500 Hz and is approaching a stationary person with
speed  ms–1. The velocity of sound in air is 300 ms–1. If the person can hear frequencies upto a
maximum of 10,000 Hz. The maximum value of  upto which he can hear the whistle is
1) 30 ms–1 2) 15 2 ms–1 3) 15 2 ms–1 4) 15 ms–1
64. A source of sound is travelling towards a stationary observer. The frequency of sound heard by the
observer is 25% more that the actual frequency. If the speed of sound is v, that of the source is
v v v v
1) 2) 3) 4)
5 4 3 2
65. To an observer, the pitch of a stationary source of sound appears to be reduced by 20%. If the speed of
sound is 340m/s then speed and direction of the observer is
1) 86 m/s towards the source 2) 68 m/s towards the source
3) 86 m/s away from the source 4) 68 m/s away from the source
66. An observer moves towards a stationary source of sound with a velocity one–fifth of velocity of sound.
The percentage increase in apparent frequency is
1) 5% 2) 20% 3) Zero 4) 0.5%
67. When both source and listner approach each other with a velocity equal to half the velocity of sound,
the change in frequency of the sound as detected by the listner is (frequency of sound=n)
n
1) n 2) 2n 3) 4) 3n
2
68. An engine giving off whistle is moving towards a stationary observer with 50m/s speed. What will be
the ratio of the frequencies of the whistle heard when engine is approaching and receding from the
observer? (speed of sound = 350 m/s)
1) 2 : 1 2) 4 : 5 3) 4 : 3 4) 3 : 4
69. A train running at 108 km/hr towards east whistles at a frequency of 800 Hz. The frequencies heard by
a passenger sitting in the train and a person standing near the track whom the train has just passed(Speed
of Sound =330 m/s)
1) 800 Hz, 733 Hz 2) 740 Hz, 800 Hz 3) 800 Hz, 880 Hz 4) 800 Hz, 750 Hz
70. A source and a deterctor move away from each other, each with a speed of 10 m/s with respect to
ground with no wind. If the detector detects a frequency 1650 Hz of the sound coming from the source,
what is the original frequency of the source? (speed of sound = 340 m/s)
1) 750 Hz 2) 1750 Hz 3) 2000 Hz 4) 1800 Hz
71. Two trains are moving towards each other at speeds of 144 km/hr and 54 km/hr relative to the ground.
The first train sounds a whistle of frequency 600 Hz. Find the frequency of the whistle as heard by a
passenger in the second train before the trains meet. (v=340m/s)
1) 610 Hz 2) 510 Hz 3) 710 Hz 4) 170 Hz
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v
72. A Car is travelling at ms–1 and sounds horn of frequency 990 Hz. The apparent frequency heard by
10
v
a police chasing the car at ms–1 where V is velocity of sound
9
1) 990 Hz 2) 900 Hz 3) 1000 Hz 4) 0
73. A source is moving with a constant speed of 10 m/s on a circular track of 200 m. It emits a sound of
frequency 200 Hz. A listener stands at the centre of the circular track. The frequency recieved by the
listener is (velocity of sound = 340 m/s)
1) zero 2) 200 Hz 3) 190 Hz 4) 210 Hz
74. A car travels at a speed of 'a' towards a high wall. The driver sounds a horn of frequency 'n'. If V is the
velocity of sound in air, frequency of reflected sound heard by the driver is
V a V a V a V a
1) n 2) n 3) n 4) n
V a V a V V
75. The wave length of the sound produced by a source is 0.8m. If the source moves towards the stationary
listner at 32 ms–1, what is the apparent wave length of sound if the velocity of sound is 320 ms–1
1) 0.32 m 2) 0.4 m 3) 0.72 m 4) 0.80 m
76. A person going away from a factory on his scooter at a speed of 36 km/hr listens to the siren of the
factory. If the frequency of siren is 525 Hz and a wind is blowing along the direction of scooter at
36km/hr the frequency, heard by the person is (velocity of sound = 340 m/s)
1) 680 Hz 2) 510 Hz 3) 640 Hz 4) 600 Hz
Acoustics :
3
77. The absorption coefficient of a material is . The ratio of maximum to minimum current during its
4
determination by stationary wave method is
1) 8 2) 4 3) 2 4) 3
78. In a big hall of volume 30 x 20 x 10 m3, if the reverberation time is 1.7 sec. The total sound absorption
in the hall is ---- Metric Sabine
1) 6000 2) 600 3) 3000 4) 300
79. The reverberation time of a hall of volume 200m3 is 1.7sec. The reverberation time if 20 persons
having absorption 0.4 metric sabine entered the hall, nearly is
1) 1.5S 2) 1.4S 3) 1.3S 4) 1.2S
80. The volume of a room is 600 m3. The wall area of the room is 220 m2. The floor and ceiling have area
of 120 m2 each. The absorption coefficients of walls, floor and ceiling are 0.03, 0.8 and 0.06 respectively.
Calculate the reverberation time
1) 0.93 s 2) 0.5 s 3) 0.2 s 4) 1.8 s
81. If due to the entry of audience into a hall the absorption becomes 3/2 times of initial absorption the
final reverberation time, (if initial reverberation time was T) wil be
1) T 2) 3/2 T 3) 0.67 T 4) 0.75 T
82. The correct graph repressenting the relation between intensity and time when a sound of is turned on in
an enclosure and after some time it is switched off
I I I I

1) 2) 3) 4)

t t t t
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83. When a sound wave of wavelength '  ' is propagating in a medium, the maximum velocity of the
particle is equal to the velocity. The amplitude of waves is (2008-E)
  
1)  2) 3) 4)
2 2 4
84. A car is moving with a speed of72 kmph towards a hill. Car blows horn at a distance of 1800 m from
the hill. If echo is heard after 10 seconds, the speed of sound (in m/sec) is
1) 300 2) 320 3) 340 4) 360
85. The frequencies of three tunuing forks A, B and C have a relation nA > nB > nC. When the forks A and
B are sounded together the number of beats produced is n1. When A and C are sounded together the
number of beats produced is n2, then the number of beats produced when B and C are sounded together
is
n1  n 2
1) n1 + n2 2) 3) n2 – n1 4) n1 – n2
2
86. Two strings of the same material and the same area of cross – section are used in sonometer experiment.
One is loaded with 12kg and the other with 3 kg. The fundamental frequency of the first string is equal
to the first overtone of the second string. If the length of the second string is 100 cm, then the length of
the first string is
1) 300 cm 2) 200 cm 3) 100 cm 4) 50 cm
87. The speed of sound in oxygen (O2) at a certain temperature is 460 ms-1. The speed of sound in helium
(He) at the same temperature will be (assumed both gases to be ideal)
1) 1420 ms-1 2) 500 ms -1 3) 650 ms-1 4) 330 ms-1
88. A wave travelling along the x-axis is described by the equation y(x,t) = 0.005 cos (  x   t  .If the
wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then  and  in
appropriate units are
0.08 2.0 0.04 1.0 
1)   25.00 ,    2)   , 3)   ,  4)   12.50 ,  
    2.0
89. While measuring the speed of sound by performing a resonance column experiment, a student gets the
first resonace condition at a column length of 18 cm during winter.Repeating the same experiment
during summer, she measures the column length to be x cm for the second resonance. Then
1) 18 > x 2) x > 54 3) 54 > x> 36 4) 36 > x > 18
90. Two sources A and B are sending notes of frequency 680 Hz. A listener moves from A to B with a
constant velocity 'u'. If the speed of sound in air is 340 ms–1, what must be the value 'u' so that he hears
10 beats per second ?
1) 2.0 m-s–1 2) 2.5 m-s–1 3) 3.0 m-s–1 4) 3.5 m-s–1
91. Two identical piano wires have a fundamental frequency of 600 c/s when kept under the same tension.
What fractional increases in the tension of one wire will lead to the occurence of 6 beats per second
when both wires vibrate simultaneously?
1) 0.01 2) 0.02 3) 0.03 4) 0.04
92. A theatre of volume 100  40  10 m can accommodate 1000 visitors. The reverberation time of the
3

theatre when empty is 8.5 sec. If the theatre is now filled with 500 visitors, occupying the front - half
seats, the reverberation time changes to 6.2 seconds. The average absorption coefficient of each visitor
is nearly
1) 0.6 2) 0.5 3) 0.45 4) 0.7

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93. An observer is standing 500 mts away from a vertical hill. Starting from a point between the observer
and the hill, a police van moves towards the hill with uniform speed sounding a siren of frequency of
100 Hz. If the frequency of the sound heard by the observer directly from the siren is 970 Hz, the
frequency of the sound heard by the observer after reflection from the hill (Hz) is nearly (Velocity of
sound in air=330 m/s)
1) 1042 2) 1031 3) 1022 4) 1012

94. Three sound waves of equal amplitudes have frequencies (v-1), v, (v+1). They superpose to give beats.
The number of beast produced per second will be:
1) 3 2) 2 3) 1 4) 4
95. A motor cycle starts from rest and accelerates along a straight path at 2 m/s2. At the atraight point of the
motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears
the frequency of the siren at 94% of its value when the motor cycle was at rest? (Speed of sound = 330
ms -1 ) (2009-AIEEE)
1) 98 m 2) 147 m 3) 196 m 4) 49m

EXERCISE - II
Wave Equations & Basics :
1. A transverse wave of amplitude 0.5m, wavelength 1m and frequency 2 Hz is propagating in a string in
the negative x direction. The equation of this wave is
1) y  0.5sin  2 x  4t  2) y  0.5sin  2 x  4 t  3) y  0.5sin  x  2t  4) y  0.5 sin  2 x  2 t 

2. The time lag between two particles vibrating in a progressive wave seperated by a distance 20m is
0.02s. The wave velocity if the frequency of the wave is 500Hz, is
1) 1000 ms-1 2) 500 ms-1 3) 2000 ms-1 4) 250 ms-1
3. Avibrating tuning fork generates a wave given by y  0.1sin (0.1x  2t) where x and y are in metre
and time ' t 'in second. The distance travelled by the wave while the fork completes 30 vibrations is
1) 600 m 2) 20 m 3) 36 m 4) 200 m
 2x   2x 
4. The path difference betweent the two waves y1  a1 sin   t   and y 2  a 2 cos   t    is
    
    2   2
1)  2)    3)    4) 
2 2  2    2  
5. The maximum particle velocity is 3 times the wave velocity of a progressive wave. If the amplitude of
the particle is "a". The phase difference between the two particles seperated by a distance of 'x' is
x 3x 3a 3x
1) 2) 3) 4)
a a x a

 x
6. The equation of a stationary wave is y  4sin   Cos 100  t  . The wave is formed using a string of
5
length 20cm. The second and 3rd antinodes are located at positions (in cm)
1) 7.5, 12.5 2) 2.5, 7.5 3) 12.5, 17.5 4) 5, 10
7. A wave y = a sin (wt–kx) on a string meets with another wave producing a node at x = 0. The equation
of the unknown wave is
1) y = a sin (wt + kx) 2) y = a cos (kx – wt) 3) y = – a cos (kx – wt) 4) y = – a sin (kx + wt)
AKASH MULTIMEDIA   IIT - VOL - 2  11
WAVE MOTION PHYSICS

8. The ends of a stretched wire of length 'L' are fixed at x = 0 and x = L. In one experiment, the displacement
x
of the wire is y1  A sin sin wt and the energy is E1, and in another experiment its displacement is
L
2 x
y2  A sin sin 2 wt and the energy is E2 then
L
1) E2 = E1 2) E2 = 2E1 3) E2 = 4E1 4) E2 = 16E1
Strings :
9. A stretched string is 1m long. Its linear density is 0.5 gm/m. It is stretched with a force of 20N. If
plucked at a distance of 25cm from one end, the frequency of the tone emitted by it is
1) 100 Hz 2) 200 Hz 3) 300 Hz 4) 400 Hz
10. A sonometer wire vibrating in fundamental mode is in unision with a tuning fork. Keeping the same
tension, the length of the wire between the bridges is doubled. the tuning fork can still be in resonance
with the wire. Provided the wire now vibrates in
1) 4 segments 2) 6 segments 3) 3 segments 4) 2 segments
11. String B has twice the length, twice the diameter, twice the tension and twice the density of string A.
The overtone of B that will be in unison with fundamental frequency of A is
1) 1st 2) 2nd 3) 3rd 4) 4th
12. Transverse waves are generated in two uniform wires A and B of the same material by attaching their
free ends to a vibrating source of frequency 200 Hz. The Area of cross section of A is half that of B
while tension on A is twice than on B. The ratio of wavelengths of the transverse waves in A and B is
1) 1 : 2 2) 2 : 1 3) 1 : 2 4) 2 : 1
13. A string is taken and stretched so that is elongates by 2%. Then its fundamental frequency
1) increases by 2% 2) decreases by 2% 3) increases by 1% 4) decreases by 1%
14. If n1,n2 and n3 be the frequencies of the segments of stretched string, find out the frequency n of the
string itself in terms of n1,n2 and n3
n1 n 2 n 3 n1 n 2  n 2 n 3  n 3 n1 n1 n 2 n 3 n1 n 2 n 3
1) n  n  n 2) n1 n 2 n 3 3) n n  n n  n n 4) n n  n n  n n
1 2 3 1 2 2 3 3 1 1 1 2 2 3 3

15. A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length
is decreased by 45% and tension is increased by 21%. Now its fundamental frequency
1) increases by 50% 2) increases by 100%
3) decreases by 50% 4) decreases by 25%
16. A sonometer wire vibrates with a frequency of 80 Hz when the tensions is T1 and with a frequency of
150 Hz when the tenison is T2, when the tension is (T1+T2) its frequency of vibration (in Hz)
1) 170 2) 230 3) 240 4) 210
17. A transverse wave propogations on a stretched string of linear density 3  10 4 kg / m is represented by
equation y = 0.2 Sin(1.5 x + 60 t) where ' x ' is in meters and ' t ' is in seconds. The tension in string (in
newtons) is
1) 0.24 2) 0.48 3) 1.20 4) 1.80
18. The Equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by
y = 2 sin (0.6x) cos (500  t) (x , y are in cm 't' is in sec). The length of the string is.
1) 24.6 cm 2) 12.5 cm 3) 20.6 cm 4) 15.7 cm
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PHYSICS WAVE MOTION

19. A steel wire of length 1m, mass 0.1kg and uniform cross sectional area 10-6 m2 is rigidly fixed at both
ends. The temperature of the wire is lowered by 20°C. If the transverse waves are set up plucking the
string in the middle, calculate the frequency of the fundamental mode of vibration. (Y = 2x1011 N/m2,
a = 1.21 x 10–5/°C)
1) 22 Hz 2) 33 Hz 3) 44 Hz 4) 11 Hz
20. A wire of density 9  103 kg / m 3 is stretched between two clamps 1 m apart and is subjected to an
extension of 4.9  10 4 m . If Young's modulus of the wire is 9  1010 N / m 2 , the lowest frequency of
the transverse vibration in the wire is
1) 35 Hz 2) 70 Hz 3) 105 Hz 4) 140 Hz
21. A metallic wire with tension T and at temperature 300C vibrates with its fundamental frequency of 1 KHz.
The same wire the same tension but at 100C temperature vibrates with a fundamental frequency of
1.001 KHz. The coefficient of linear expanasion of the wire is (2002 E)
1) 2  10 /ºC
-4
2) 1.5  10 /ºC
-4
3) 1  10 /ºC
-4
4) 0.5  10 /ºC
-4

22. The extension in a string, obeying Hooke's law, is x. The speed of sound in the stretched string is v. If
the extension in the string is increased to 1.5 x, the speed of sound will be
1) 1.22 v 2) 1.61 v 3) 1.50 v 4) 0.75 v
23. Two wires of radii r and 2r are welded together end to end. The combination is used as a sonometer
wire and is kept under a tension T. The welded point is midway between the bridges. The ratio of the
number of loops formed in the wires, such that the joint is a node when stationary vibrations are set up
in the wires, is
1 1 1 2
1) 2) 3) 4)
4 3 2 3
24. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes
between the two bridges when a mass of 9 Kg is suspended from the wire. When this mass is replaced
by a mass ' M ' the wire resonates with the same tuning fork for three antinodes for the same positions
of the bridges the value of M is
1) 25 Kg 2) 5 Kg 3) 12.5 Kg 4) 1/ 25 Kg
25. A sonometer wire of 70cm length fixed at one end has a solid mass M, hanging from its other end to
produce tension in it. The wire produces a certian frequency. When the same mass 'M' hange in water,
it is found that the length of the wire has to be changed by 5 cm. in order to produce the same
frequency. Then the density of the material of mass 'M' is
169 196
1) gm / c.c 2) 1 gm / c.c 3) 5 gm / c.c 4) gm / c.c
27 27
26. Two strings A and B of lengths, LA = 80 cm and LB = x cm respectively are using separately in a
 dA 
sonometer. The ratio of their densities  d  is 0.81. The diameter of B is one-half that of A. If the
B
strings have the same tension and same fundamental frequency then the value of x is :
1) 33 2) 102 3) 144 4) 130
Velocity of Sound :
27. Two monoatomic ideal gases 1 and 2 of molecules masses m1 and m2 respectively are enclosed in
separate container kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas
'2' is given by
m1 m2 m1 m2
1) m2
2) m1
3) m 4) m
2 1

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WAVE MOTION PHYSICS

28. The ratio of densities of nitrogen and oxygen is 14 : 16. The temperature at which the speed of sound
in nitrogen will be same as that in oxygen at 550C is (EAMCET 99 E)
1) 35 C0
2) 48 C0
3) 65 C0
4) 14 C
0

29. A sample of oxygen at NTP has volume V and a sample of hydrogen at NTP has the volume 4V. Both
the gases are mixed. If the speed of sound in hydrogen at NTP is 1270 m/s, that in mixture is
1) 317 m/s 2) 635 m/s 3) 830 m/s 4) 950 m/s
30. A tuning fork produces a wave of wavelength 110 cm in air at 00C. The wavelength at 250C would be
1) 110 cm 2) 115 cm 3) 120 cm 4) 130 cm
Pipes :
31. An open pipe is suddenly closed at one end as a result, frequency of third harmonic of the closed pipe
is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental
frequency of the open pipe is
1) 200 Hz 2) 300 Hz 3) 240 Hz 4) 480 Hz
32. The fundamental frequencies of a closed pipe and an open pipe of different lengths are 300 Hz and 400
Hz respectively. If they are joined to form a longer pipe, the fundamental frequency of the long pipe so
formed is
1) 350 Hz 2) 50 Hz 3) 120 Hz 4) 100 Hz
33. Two tuning forks A and B give 5 beats/s. A resonates with a column of air 15 cm long, closed at one
end, and B with a column 30.5 long, open at both ends. Neglecting end correction, the frequencies of
A and B are respectively
1) 305, 295 Hz 2) 295 Hz, 300 Hz 3) 305 Hz, 300 Hz 4) 300 Hz, 305 Hz
34. A closed organ pipe and an open organ pipe of same length produce 2 beats per sec when they are set
into vibrations simultaneously in the fundamental mode. The length of open pipe is now haved and of
closed pipe is doubled, the number of beats produced will be
1) 8 2) 7 3) 4 4) 2
35. A glass tube of 1.0 m length is filled with water. The water can be drained out slowly at the bottom of
the tube. If a vibrating tuning fork of frequency 500 c/s is brought at the upper end of the tube and the
velocity of sound is 330 m/s, then the total number of resonances obtained will be
1) 4 2) 3 3) 2 4) 1
36. The frequency of a stretched uniform wire under tension is in resonance with the fundamental frequency
of a closed tube. If the tension in the wire is increased by 8 N, It is in resonance with the first overtone
of the closed tube. The initial tension in the wire is
1) 1 N 2) 4 N 3) 8 N 4) 16 N
37. Two closed pipes produces 10 beats per second when emitting their fundamental nodes. If their lengths
are in ratio of 25 : 26. Then their fundamental frequencies in Hz are
1) 270, 280 2) 260, 270 3) 260, 250 4) 260, 280
38. A Source of frequency 10 KHz, when vibrated over the mouth of a closed organ pipe is in unison at
300K. The beats produced when temperature rises by 1K is
1) 30 Hz 2) 13.33 Hz 3) 16.67 Hz 4) 40 Hz
Beats :
39. Wavelengths of two notes in air are 80/175 m and 80/173 m. Each note produces 4 beats/s. with a third
note of a fixed frequency. The speed of sound in air is
1) 400 m/s 2) 300 m/s 3) 280 m/s 4) 320 m/s
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PHYSICS WAVE MOTION

40. Two identical sonometer wires have a fundamental frequency of 400 vibrations per second when kept
under the same tension. What fractional increase in the tension of one wire would cause an occurance
of 8 beats per second when both wires vibrate together
1) 0.02 2) 0.03 3) 0.01 4) 0.04
41. A tuning fork of frequency 250Hz produces 4 beats per second with a wire of length 25cm vibrating in
its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could
be the minimum length by which the wire be shortened so that it produces no beats with the tuning
fork?
1) 0.2 cm 2) 0.4 cm 3) 0.3 cm 4) 0.1 cm
42. A tuning fork gives 4 beats with 50 cm length of a sonometer wire. If the length of the wire is shortened
by 1cm the number of beats is still the same. the frequency of the fork is
1) 396Hz 2) 400Hz 3) 404Hz 4) 384Hz
43. The string of a sonometer is divided into two parts with the help of a wedge. The total length of the
string is 1m and the two parts differ by 2mm. When sounded together they produced two beats per
second. The frequencies of the notes emitted by the two parts are
1) 499 & 497 Hz 2) 501 & 499 Hz 3) 501 & 503 Hz 4) none
44. When two tuning forks are vibrated together 5 beats per second are heard. One tuning fork is in unision
with a wire of length 50 cm other tuning fork is in unision with the wire when length increases by 1 cm.
The frequency of the forks are
1) 255 Hz, 250 Hz 2) 300 Hz, 295 Hz 3) 195 Hz, 190 Hz 4) 500 Hz, 555 Hz
45. When tension in the string is 100N, it gives 5 beats with a tuning fork. When tension is changed to 81
N again it gives 5 beats with same tuning fork. The frequency of the fork is
1) 90 Hz 2) 95 Hz 3) 100 Hz 4) 110 Hz
46. Two uniform wire are vibrating simultaneously in their fundamental modes. The tensions, lengths,
diameters, and the densities of the two wires are in the ratios, 8:1 ; 36:35 ; 4:1 ; 1:2 respectively. If the
note of higher pitch has a frequency of 360Hz the number of beats produced per second is
1) 5 2) 10 3) 15 4) 20
Echoes :
47. A soldier walks towards a high wall taking 120 steps per minute. When he is at a distance of 90 m from
the wall he observes that echo of step coincides with the next step. The speed of sound must be
1) 340 m/s 2) 330 m/s 3) 300 m/s 4) 360 m/s
48. A man standing midway between two cliffs claps his hands and starts hearing a series of echoes at
intervals of 1s. The speed of sound in air is 340 m/s the distance between the cliffs must be
1) 340 m 2) 680 m 3) 1020 m 4) 170 m
49. A road runs midway between two parallel rows of buildings. A motorist moving with a speed of 36 Km
/ h sounds the horn. He hears the echo one second after he has sounded the horn. Then the distance
between the two rows of buildings is. (Velocity of sound in air is 330 m/s)
1) 80 17 m 2) 40 17 m 3) 30 10 m 4) 34 10 m
Doppler effect :
50. When a train is approaching the stationary observer, the apparent frequency of the whistle observed as
100 Hz, while when it has passed away from the observer with same speed, it is 50 Hz. Calculate the
frequency of the whistle when the observer moves with the train (V = 330 m/s)
1) 33.3 Hz 2) 50 Hz 3) 66.6 Hz 4) 75 Hz
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WAVE MOTION PHYSICS

51. A vehicle sounding a whistle of frequency 256 Hz is moving on a straight road, towards a hill with
a velocity of 10 m/s. The number of beats produced per second is (Velocity of sound = 330 m/s)
1) Zero 2) 10 3) 14 4) 16
52. A person is listening to two trains one approaching him while the other moving away from him. The
speed of both the trains is 5 m/s. If both trains give off whistle of their natural frequency of 280 Hz then
the observer will hear ........ no of beats/s. (Velocity of sound = 350 m/s)
1) 6 2) 7 3) 5 4) 8
53. Two sources A and B are sounding notes of frequency 700 Hz. A listener moves from A to B with
constant velocity u. If the speed of sound is 350 m/s, what must be the value of u so that 8 beat/s are
heard
1) 2 m/s 2) 1.5 m/s 3) 2.5 m/s 4) 4 m/s
54. A person is standing between two tuning forks each vibrating at 240 Hz. If both the forks move towards
right at a speed of 5.5 m/s find the number of beats heard by the person (speed of sound = 330 m/s)
1) 3 2) 6 3) 8 4) 9
55. Two stationary sources A and B produces sounds of same frequency. A person running from A to B
hears 6 beats/s. If the frequency of each source increases by 100 Hz then 8 beats/s are heard. Then the
original frequency of each source is
1) 150 Hz 2) 200 Hz 3) 300 Hz 4) 100 Hz
56. Two different sound sources s1 and s2 have frequencies ratio 1:2. Source s1 is approaching towards an
observer and s2 is receding from the same observer. Speeds of both s1 and s2 are the same and equal to
v . speed of sound in air in 300 m / s. If no beats are heard by the observer the value of V is
1) 125 m / s 2) 100 m / s 3) 75 m / s 4) 50 m / s
57. A source of sound and an observer are approaching each other with the same speed, which is equal to
1
  times the speed of sound. The apparent relative change in frequency of source is (2005 M)
 10 
1) 22.2% increases 2) 22.2% decreases 3) 18.2% decreases 4) 18.2% increases
58. A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a
moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return
journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The
ratio of velocity of train B to that of train A is
242
1) 2) 2 3) 5/6 4) 11/6
252
59. A police car moving at 22 m/s chases a motorcyclist. The police man sounds his horn at 176 Hz, while
both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle.
If it is given that the motorcyclist does not observe any beats (Velocity of sound = 330 m/s)
1) 33 m/s 2) 22 m/s 3) zero 4) 11 m/s
60. A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity 17
ms-1. The apparent change in the wavelength of sound heard by the observer (speed of sound in air
=340ms -1)
1) 0.1m 2) 0.2 m 3) 0.4 m 4) 0.5 m
61. A radar sends a radio signal of frequency 9  10 Hz towards an aircraft approaching the radar. If the
9

reflected wave shows a frequency shift of 3  103Hz the speed with wich the aircraft is approaching the
radar in ms–1 (velocity of the rador signal is 3  108 ms–1)
1) 150 2) 100 3) 50 4) 25

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PHYSICS WAVE MOTION

62. A train is moving at 30 m/s in still air. The frequency of the locomotive whistle is 500 Hz and the speed
of sound is 345 m/s.what would be the apparent wavelengths in front of and behind the locomotive if
a wind of speed 10 m/s were blowing in the same direction as that in which the locomotive is travelling?
1) 0.65 m , 0.73 m 2) 0.60 m , 0.73 m 3) 0.65 m , 0.78 m 4) 0.60 m , 0.71 m
63. An observer is standing 500 m away from a vertical hill. Starting between the observer and the hill, a
police van sounding a siren of frequency 1000 Hz moves towards the hill with a uniform speed. If the
frequency of the sound heard directly from the siren is 970 Hz, the frequency of the sound heard after
reflection from the hill (in Hz) is about, (velocity of sound = 330 ms-1)
1) 1042 2) 1032 3) 1022 4) 1012
64. A car travelling at a speed of 54 km/hr towards a large wall horns a sound of frequency 400 Hz. A
person standing between the car and the wall recieves sounds one directly from the car and the other
reflected from the wall. The number of beats heard by him per second are
1) 8 2) 6 3) 3 4) zero
65. A car travelling at a speed of 54 km/hr towards a large wall horns a sound of frequency 400 Hz if the
person stands behind the car such that the car receding from him approaches the wall the difference in
frequencies of the two sounds one recieved directly from the car and the other reflected from the wall
(speed of sound is 335 m/s)
1) 35.9 Hz 2) 20 Hz 3) 70 Hz 4) 30 Hz
66. A train approaching a railway crossing at a speed of 120 km/hr sounds a whistle of frequency 640 Hz
when it is 300 m away from the crossing. What will be the frequency heard by person standing on a
road perpendicular to the track through the crossing at a distance of 400 m from the crossing
( v = 340 m/s)
1) 600 Hz 2) 680 Hz 3) 620 Hz 4) 660 Hz
67. The difference between the apparent frequencies of a source of sound as perceived by a stationary
observer during its approach and recession is 2%of the actual frequency of the source. If the speed of
sound is 300 m/s, the speed of the source is
1) 12 m/s 2) 6 m/s 3) 1.5 m/s 4) 3 m/s
68. When a source of sound approaches a stationary observer with a constant speed V s , the apparent
increase in the frequency of the sound is found to be x%. If the same source recedes away from the
same observer with the same speed Vs, the apparent change in the frequency will
1) > x% 2) < x% 3) = x% 4)  x%
69. A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 rad/
s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air
is 330 ms–1).
1) 509 Hz 2) 594 Hz 3) 598 Hz 4) 602 Hz
Acoustics :
1
70. The ratio of the absorption of the person to that the auditorium is . In order to make the reverberation
1500
3
time th of the initial value the number of persons to be accommodated in the auditorium is
5
1) 1000 2) 500 3) 1500 4) 750

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WAVE MOTION PHYSICS

71. The reverberation time of an empty auditorium is 3.0 sec. If becomes 2 sec when 'N' number of audience
enter the auditorium. The reverberation time, when 'N' more number of audience enter the same
auditorium, is
1) 1/2 sec 2) 1 sec 3) 1.5 sec 4) 1.75 sec
72. The total absorption of an auditorium is 3000 metric Sabine. When a material of area 1000sq.m is
brought into the auditorium the reverberation time decreases from 2s to 1.8s. The absorption coefficient
of the material brought is
1) 2) 3) 4)

LEVEL - I ANSWERS
EXERCISE - I
1) 3 2) 2 3) 1 4) 1 5) 3 6) 2 7) 3 8)4 9) 2 10) 2
11) 2 12) 1 13) 3 14) 3 15) 3 16) 3 17) 1 18) 1 19) 4 20) 3
21) 4 22) 2 23) 4 24) 2 25) 2 26) 3 27) 3 28) 1 29) 2 30) 3
31) 2 32) 2 33) 2 34) 3 35) 3 36) 2 37) 2 38) 4 39) 3 40) 1
41) 3 42) 3 43) 4 44) 1 45) 2 46) 1 47) 3 48) 2 49) 3 50) 1
51) 3 52) 2 53) 3 54) 1 55) 2 56) 3 57) 2 58) 1 59) 4 60) 2
61) 4 62) 3 63) 4 64) 1 65) 4 66) 2 67) 2 68) 3 69) 1 70) 2
71) 3 72) 3 73) 2 74) 1 75) 3 76) 2 77) 4 78) 2 79) 4 80) 1
81) 3 82) 4 83) 3 84) 2 85) 3 86) 3 87) 1 88) 1 89) 2 90) 2
91) 2 92) 1 93) 2 94) 2 95) 1

EXERCISE - II
1) 2 2) 1 3) 1 4) 2 5) 2 6) 1 7) 4 8) 3 9) 2 10) 4
11) 3 12) 4 13) 4 14) 3 15) 2 16) 1 17) 2 18) 4 19) 4 20) 1
21) 3 22) 1 23) 3 24) 1 25) 4 26) 3 27) 2 28) 4 29) 2 30) 2
31) 1 32) 3 33) 3 34) 2 35) 2 36) 1 37) 3 38) 3 39) 4 40) 4
41) 2 42) 1 43) 2 44) 1 45) 2 46) 2 47) 4 48) 1 49) 1 50) 3
51) 4 52) 4 53) 1 54) 3 55) 3 56) 2 57) 1 58) 2 59) 2 60) 1
61) 3 62) 1 63) 2 64) 4 65) 1 66) 2 67) 4 68) 2 69) 2 70) 1
71) 3 72) 1

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PHYSICS WAVE MOTION

LECTURE SHEET

nLEVEL -II
EXERCISE - I
o
(Single & One or More than One Correct Answers)
Pulse and wave equations :
1. Which of the following functions represent a travelling wave
1
a)  x  vt  b)  x  vt 
2 2
c) e  x  vt 
2
d)
x  vt
2. The displacement of the particle at x = 0 of a streached string carrying a wave in the positive

 t 
x-direction is given by f(t)= A sin   . The wave speed is V. Write the wave equation
T

 t x t x 
a) f  x, t   A sin    b) f  x, t   A sin   
T V T VT 

 x  t x 
c) f  x, t   A sin  t   d) f  x, t   A sin   
VT  T VT 
3. The equation of a wave travelling on a string stretched along the x-axis is given by
2
x t
  
y  Ae a T where A, a and T are constants of apPropriate dimensions

a) The speed of the wave is a/T.

b)The wave is travelling along negative x- axis
c) The maximum of the pulse located at t = T is x = -a
d) The maximum of the pulse located at t = 2T is x = -2a

a3
4. A pulse travelling on a string is represented by the function y  where x = 5 mm and
 x  vt  2  a 2
v= 20 cm/s where the maximum of pulse is located at t=0, 1s and 2s. Take x=0 in the middle of the
string
a) x = 0, 20 cm and 40 cm b) x = 20 m, 40 cm and 60 cm
c) x=10 m, 20 cm and 30 cm d) x = 4cm, 10 cm and 15 cm
5. A motion is described by y  3e x .e 3t where y, x are in metre and t is in seconds.

a) This represents equation of progressive wave propagating along -x direction with 3ms 1
b) This represents equation of progressive wave propagating along +x direction with 3ms 1
c) This does not represent a progressive wave equation.
d) Date is insufficient to arrive at any conclusion of this sort.

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WAVE MOTION PHYSICS

6. The equation of a wave travelling along the positive x-axis, as shown in figure at t = 0 is given by
  y
   kx  t  
a) 1sin  kx  t   b) 1sin  6 1
 6
0 x
    -0.5
c) 1sin  t  kx   d) 1sin  t  kx  
 6  6
-1
Waves in stretched string :
7. Figure shows the shape of part of a long string in which transverse waves are produced by attaching
one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?
a) 1.0 ms–1
b) 1.5 ms–1
c) 2.0 ms–1
d) 2.5 ms–1
8. A wire of 10–2 kgm–1 passes over a frictionless light pulley fixed on the top of a frictionless inclined
plane which makes an angle of 30° with the horizontal. Masses m and M are tied at two ends of wire
such that m rests on the plane and M hangs freely vertically downwards. The entire system is in
equilibrium and a transverse wave propagates along the wire with a velocity of 100 ms–1. Then

m 1 m
a) M = 5 kg b) = c) m = 20 kg d) =4
M 4 M
9. A long rope is design as shown in the figure such away that v independent of z is distance from point
of suspension. For such a rope  cannot be constant. Where  is leniar density of rope. what is the
general equation for   z  [use 0 as mass per unit length of the rope
at point z  0 ]


2
a)   4 0 e  (g /  )z
__ z

b)    0 e  g /  z 
2 dz

2
c)   4 0 e(g /  )z

d)   4 0 e
 g /  z
4

10. A string of length L consists of two distinct sections. The left half has linear mass density 1   0 / 2 ,
while the right half has linear mass density  2  30 . Tension in the string is Fo. The time required for
a transverse wave pulse to travel from one end of the string to the other is
L o L 2 o L o L o
a) 4 F ( 2  6) b) 2 F (1  3) c) 2 2F ( 2  6) d) 2 2F (1  6)
o o o o

11. A stretched string is taken and stretched show that elongated by 1% then the fundamental frequency
a) increases by 0.5% b) decreases by 0.5%
c) increases by 1% d) decreases by 1%

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12. A maxture of two diatomic gases exists in a closed cylinder. The volumes and velocity of sound in the
two gases are V1, V2, c1 and c2 respectively. Determine the velocity of sound in the gaseous mixture.
( Pressure of gas remains constant)

V1  V2 V22  V12 V2  V1 V2  V1
a) c1c 2 b) c 2 c1 c) c 2 c1 d) c1c 2
V1c 22  V2 c12 V1c 22  V2 c12 V1c 22  V2 c12 V1c12  V2 c 22

13. A stiff wire is bent into a circular loop of diameter D. It is clamped by knife edges at two points opposite
to each other.A transverse wave is sent around the loop by means of a small vibrator which acts close
to one clamp. The resonance frequency (fundamental mode) of the loop in terms of wave speed v and
diameter D is
v 2v v v
a) b) c) d)
D D D 2 D
14. A sonometer wire fixed at one end has a solid mass M haging from its other end to produce tension in
it. It is found that 70 cm length of the wire produces a certain fundamental frequency when plucked.
When the same mass M is hanging in water completely submerged in it, it is found that the length of the
wire has to be changed by 5 cm in order that it will produce the same fundmental frequency. Calculate
the density of the material of mass M.
a) 7.26  10 4 kg / m 3 b) 7.62  10 5 kg / m 3 c) 5.14  10 4 kg / m 3 d) 7.26  10 3 kg / m 3
15. A long wire PQR is made by joining two wires PQ and QR of equal radii. PQ has length 4.8 m and mass
0.06 kg. QR has length 2.56 m and mass 0.2 kg. The wire PQR is under a tension of 80 N. A sinusoidal
wave-pulse of amplitude 3.5 cm is sent along the wire PQ from the end P. No power is dissipated
during the propagation of the wave-pulse. Calculate
A) the time taken by the wave -pulse to reach the other end R of the wire and
B) the amplitude of the reflected and transmitted wave pulses after the incident wave pulse cross the
joint Q.
a) 0.14 s, 1.5 cm, 2 cm b) 0.3 s, 1.2 cm, 2 cm
c) 0.4 s, 1.3 cm, 1 cm d) 0.2 s, 1.1 cm, 3 cm
16. A steel wire of length 1 m, mass 0.1 kg and uniform cross-sectional area 10–6 m2 is rigidly fixed at both
ends. The temperature of the wire is lowered by 200C . If the transverse waves are set up by plucking
the string in the middle, calculate the frequency of the fundamental mode of vibration.
[Y  2  1011 N / m 2 and   1.21  10 5 / 0 C ]
a) 21 Hz b) 31 Hz c) 11 Hz d) 1 Hz
Transmitted & reflected waves :
17. A pulse shown here is reflected from the rigid wall A and then from free end B. The shape of the string
after these 2 reflection will be

a) b) c) d)

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18. A composition string is made up by joining two strings of different masses per unit length 1g/ m
and 4 g/m. The composite string is under the same tension. A transverse wave pulse : Y = (6 mm)
sin(5t + 40x), where ‘t’ is in seconds and ‘x’ in meters, is sent along the lighter string towards the
joint. The joint is at x = 0. The equation of the wave pulse reflected from the joint is
a) (2 mm) sin(5t – 40x) b) (4 mm) sin(40x – 5t)
c) – (2 mm) sin(5t – 40x) d) (2 mm) sin (5t – 10x)
Intensity, power & interference :
19. A point isotropic source is located on the perpendicular to the plane of a ring drawn through the centre
O of the ring. The distance between the point O and the source is l  1 m , the radius of the ring is
R  0.50 m . Find the mean energy flow across the area enclosed by the ring if at the point O the
intensity of sound is equal to I 0  30 W / m 2 .
a)  '  20 W b)  '  30 W c)  '  50 W d)  '  80 W
20. How many times more intense is 90 dB sound than 40 dB sound?
a) 5 b) 50 c) 500 d) 105
21. The faintest sound the human ear can detect at a frequency of 1 kHz (for which the ear is most sensitive)
corresponds to an intensity of about 10 12 W / m 2 (the so called threshold of hearing). Determine the
pressure amplitude and maximum displacement associated with this sound assuming the density of
air = 1.3 kg / m3 and velocity of sound in air = 332 m/s

a) 2.94  10 5 N / m 2 , 1.1  10 11 m b) 2.94  10 4 N / m 2 , 1.3  10 11 m

c) 2.94  10 1 N / m 2 , 1.2  10 11 m d) 2.94  10 3 N / m 2 , 1.5  10 11 m

22. A standing wave is maintained in a homogeneous string of cross-sectional area s and density  . It is
formed by the superposition of two waves-travelling in opposite directions given by the equation
y1  a sin  t  kx and y2  2 a sin  t  kx  . The total mechanical energy confined between the
sections corresponding to the adjacent antinodes is
3s 2 a 2 s 2 a 2 5s 2 a 2 2 s 2 a 2
a) b) c) d)
2k 2k 2k 2k
23. A dog while barking delivers about 1 mW of power. If this power is uniformly distributed over a
hemispherical area, what is the sound level at a distance of 5 m? What would the sound level be if
instead of 1 dog, 5 dogs start barking at the same time each delivering 1 mW of power
a) 68 dB, 75 dB b) 58 dB, 68 dB c) 48 dB, 58 dB d) 38 dB, 28 dB

24. A blast gives a sound of intensity 0.80 W / m 2 and frequency 1 kHz. If the density of air is 1.3 kg / m3
and speed of sound in air is 330 m/s find the amplitude of the sound wave
a) 9.6´ 10 - 6 m b) 9.6  1011 m c) 9.7  10 11 m d) 9.7  10 16 m
25. A person standing at a distance of 6 m from a source of sound receives sound wave in two ways, one
directly from the source and other after reflection from a rigid boundary as shown in the figure. The
maximum wavelength for which, the person will receive maximum sound intensity, is
16 8
a) 4 m b) m c) 2 m d) m
3 3
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26. A plane longitudinal wave having angular frequency w = 500 rad / sec is travelling in positive x-direction
in a medium of density   1 kg / m3 and bulk modulus 4  10 4 N / m 2 . The loudness at a point in the
medium is observed to be 20 dB. Assuming at x = 0 initial phase of the medium particles to be zero,
find
A) maximum pressure change in the medium B) the equation of the wave
 5x 
a) 2  10 4 N / m 2 , y  2  10 9 sin  500t  
5x 9
b) 2  10 4 N / m 2 , y  3  10 sin  500t  
 2 2

 5x 
c) 3  10 4 N / m 2 , y  3  10 9 sin  500t  5x  d) 1  10 3 N / m 2 , y  2  10 9 sin  5000t  
 2   2

27. Two sounding bodies are producing progressive waves given by y1  4sin  400 t  and y2  3sin  404 t  ,
where t is in second which superpose near the ears of a person. The person will heard.
4
a) 2 beats per second withintensity ratio between maxima and minima.
3
b) 2 beats per second with intensity ratio 49 between maxima and minima
c) 4 beats per second with intensity ratio 7 between maxima and minima
4
d) 4 beats per second with intensity ratio between maxima and minima
3
28. Two sources of sound S1 and S2 vibrate at the same frequency and are in phase. The intensity of sound
detected at a point P (as shown in figure) is I0.

 

S1 S2

A) If   450 , what will be the intensity of sound detected at this point if one of the sources is switched off ?
B) What will be the intensity of sound detected at P if   60 0 and both the sources are now switched on ?
I0 I0 I0 I1
a) , I0 b) , I0 c) , I0 d) , I 0
4 3 5 5
Organ pipes :
29. An open organ pipe of length L vibrates in second harmonic mode. The pressure vibration is maximum
a) at the two ends b) at a distance L/4 from either end inside the tube
c) at the mid-point of the tube d) none of these
30. A tuning fork of frequency 340 Hz is vibrated just above a cylindrical tube of length 120 cm. Water is
slowly poured in the tube. If the speed of sound is 340 ms–1 then the minimum height of water required
for resonance is:
a) 95 cm b) 75 cm c) 45 cm d) 25 cm
31. In a closed end pipe of length 105 cm, standing waves are set up corresponding to the third overtone.
What distance from the closed end, amongst the following, is a pressure Node?
a) 20 cm b) 60 cm c) 85 cm d) 45 cm

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32. In case of closed organ pipe which harmonic the pth overtone will be
a) 2p + 1 b) 2p - 1 c) p + 1 d) p - 1
33. First overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open
organ pipe. Further nth harmonic of closed organ pipe is also equal to the mth harmonic of open pipe,
where n and m are:
a) 5, 4 b) 7, 5 c) 9, 6 d) 7, 3
34. The first resonance length of a resonance tube is 40 cm and the second resonance length is 122 cm. The
third resonance length of the tube will be
a) 200 cm b) 202 cm c) 203 cm d) 204 cm
35. A gas is filled in an organ pipe and it is sounded with an organ pipe in fundamental mode. Choose the
correct statement(s) : (T = constant)
a) If gas is changed from H2 to O2, the resonant frequency will increase
b) If gas is changed from O2 to N2, the resonant frequency will increase
c) If gas is changed from N2 to He, the resonant frequency will decrease
d) If gas is changed from He to CH4, the resonant frequency will decrease
36. For a certain organ pipe three successive resonance frequencies are observed at 425 Hz, 595 Hz and
765 Hz respectively. If the speed of sound in air is 340 m/s, then the length of the pipe is:
a) 2.0 m b) 0.4 m c) 1.0 m d) 0.2 m
37. In a resonance-column experiment, a long tube, open at the top, is clamped vertically. By a separate
device water level inside the tube can be moved up or down. The section of the tube from the open end
to the water level acts as closed organ pipe. A vibrating tuning fork is held above the open, and the
water level is gradully pushed down. The first and the second resonances occur when the water levelis
24.1 cm and 74.1cm respectively below the open end. The diameter of the tube is
a) 2 cm b) 3 cm c) 4 cm d) 5 cm
38. A wire of length 40 cm which has a mass of 4 gms oscillates in its second harmonic and sets the air
column in the tube to vibrations in its fundamental mode as shown in figure. Assuming speed of sound
in air as 340 m/s, find the tension int wh wire. 40 cm

a) 11.56 N
b) 12.54 N
1m
c) 13. 46 N
d) 11. 36 N
Beats :
39. The first overtone of an organ pipe beats with the first overtone of a closed organ pipe with a beat
frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. Find the lengths
of the open pipes. (Speed of sound v = 330 m/s)
a) l0  3.8937 m b) l0  1.9937 m c) l0  0.9937 m d) l0  2.8937 m
40. An unknown frequency x produces 8 beats per second with a frequency of 250 Hz and 12 beats
with 270 Hz source then x is :
a) 258 Hz b) 242 Hz c) 262 Hz d) 282 Hz

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41. Two tuning forks A & B produce notes of frequencies 256 Hz & 262 Hz respectively. An unknown
note sounded at the same time as A produces beats . When the same note is sounded with B, beat
frequency is twice as large . The unknown frequency could be :
a) 268 Hz or 260 Hz b) 260 Hz or 252 Hz c) 250 Hz or 258 Hz d) 242 Hz or 250 Hz
42. The speed of sound in a gas, in which two waves of wavelength 1.0 m and 1.02 m produce 6 beats per
second, is approximately:
a) 350 m/s b) 306 m/s c) 380 m/s d) 410 m/s
43. A string under a tension of 129.6 N produces 10 beats per sec when it is vibrated along with a tuning
fork. When the tension in the string is increased to 160 N, it sounds in unison with the same tuning fork.
Calcualte the fundamental frequency of the tuning fork
a) 100 Hz b) 200 Hz c) 300 Hz d) 400 Hz
Doppler effect :
44. A source emitting a sound of frequency V is placed at a large distance from an observer. The source
starts moving towards the observer with a uniform acceleration a. Find the frequency heard by the
oserver corresponding to the wave emitted just after the source starts. The speed of sound in the
medium is u.

V2 2V2  2V 2V2

a) b) c) d)
2V  a 2V  a V  a 2V  a
45. A source of sound emitting a note of constant frequency is moving towards a stationary listener and
then recedes from the listener with constant velocity maintained throughout the motion. The frequency
heard by the listener (f). when plotted against time (t) will give the following curve(s).

f f f f

a) b) c) d)
o t o t
o t o t

46. A stationary sound source 's' of frequency 334 Hz and a stationary observer 'O' are placed near a
reflecting surface moving away from the source with velocity 2 m/sec as shown in the figure. If the
velocity of the sound waves is air is V = 330 m/sec, the apparent frequency of the echo is
a) 332 Hz
b) 326 Hz
c) 334 Hz
d) 330 Hz
47. The frequency changes by 10% as a sound source approaches a stationary observer with constant
speed vs. What would be the percentage change in frequency as the source recedes the observer with
the same speed. Given that vs < v. (v = speed of sound in air)
a) 14.3% b) 20% c) 10.0% d) 8.33%

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48. A detector is released from rest over a source of sound of frequency f0 = 103 Hz. The frequency
observed by the detector at time t is plotted in the graph. The speed of sound in air is
(g = 10 m/s2)
a) 330 m/s
b) 350 m/s
c) 300 m/s
d) 310 m/s
49. An engine whistling at a constant frequency n0 and moving with a constant velocity goes past a stationary
observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor f.
The actual difference in the frequencies of the sound heard by him before and after the engine crosses
him is

1  1  f 
2
1  1 f  1  1 f 
a) n0(1 - f2) b) n0  c) n0   d) n  
2 2  f  1 f  2 0 1 f 

50. A stationary source of sound S having frequency f. Wind is blowing from source to observer O with
velocity u. If speed of sound with respect to air is C, the wavelength of sound detected by O is:

Cu Cu CC  u  C

a) b) c) d)
f f C  u f f
51. A train moves towards a stationary observer with34m/s.The train sounds whistle and its frequency
registered by the observer is f1 . If the train’s speed is reduced to 17m/s, the frequencyregistered is f 2 .
f1
If the speed of sound is 340m/s, then the ratio f is
2

18 1 19
a) b) c) 2 d)
19 2 18
52. A boy is sitting on a swing and blowing a whistle at a frequency of 1000 Hz. The swing is moving to an
angle of 300 from vertical. The boy is at 2m from the point of support of swing and a girl stands infront
of swing then the maximum frequency she will hear, is

300 2 m
a) 1000 Hz b) 1001 Hz

b
c) 1007 Hz d) 1011 Hz
Girl
53. A string 25 cm long and having a mass of 2.5 g is under tension. A pipe closed at one end is 40 cm
long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental
frequency, 8 beats per second are heard. It is observed that decreasing the tension in the string decreases
the beat frequency. If the speed of sound in air is 320 m/s, find the tension in the string
a) 25.03 N b) 27.04 N c) 37.01 N d) 20.02 N

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54. A source of sound emitting a frequency 660 Hz is moving counter-clockwise in a circular path of
radius 2 metres with an angular velocity 15 rad/s. A recorder at a distance from the source is moving
15
simple harmonically along a straight line with an amplitude 2 metres. The frequency of SHM is per
2
second. The arrangement is shown in figure. When the source is at point A the detector is at D. Find the
maxium and minimum frequencies recorded. Velocity of sound in air at this temperature can be taken
B
as 300 m/s F
2m
a) 870 Hz, 480 Hz b) 600 Hz, 733.4 Hz E

c) 680 Hz, 380 Hz d) 580 Hz, 280 Hz D

A

55. At t = 0, a source of sonic oscillations S and an observer O start moving along x and y axes with
velocity 5 m/s and 10 m/s respectively. The figure gives their position at t = 0. The frequency of sonic
oscillations of source is 1000 Hz. Obtain the frequency of signals recieved by the observer after 5
seconds. Speed of sound is 330 m/s.
y
a) 1020 Hz
100 m
b) 1010 Hz S X

c) 1030 Hz 100 m

O
d) 1100 Hz

56. Two stright parallel railway tracks are separated by a distance of 20 m. Two trains start simultaneously
with speeds 54 km/hr in opposite directions from A and B as shown. They have identical frequencies
of their horns which is 660 Hz. Find the frequency of the horn heard by any of the train driver due to
the other, 15 min after the start A

a) 560 Hz
20 m
b) 460 Hz
c) 360 Hz 27 km
B

d) 660 Hz

57. A square ground of side a  10 / 2 m has a circular running track of radius a / 2 with its centre coinciding
the centre of the ground. A man is running on the track with an angular velocity   22 rad / s while
a car is moving on a road adjacent to ground as shown in the figure. The car moves in such away that
the car, the man and the centre of the ground always lie on the same straight line. If a source of sound
of frequency v = 300 Hz is being placed at the centre of the ground find the minimum frequency
received by the man in the car. Assume velocity of sound in air is   330 m / s .
a) 200 Hz a

b) 210 Hz  a
2 a
c) 190 Hz
d) None

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58. By observing an alternating Doppler shift of a spectral line, the astronomers can deduce the existence
of a binary star system, which otherwise cannot be resolved visually. Suppose that an astronomical
observation shows that the source of light is eclipsed once every 18 h. The wavelength of the spectral
line observed changes for a maximum of 563 nm to a minimum of 539 nm. Assume that the binary
system consists of two identical stars. Determine the mass of each object.
 max
a) 3.69  1035 kg

b) 6.69´ 10 35 kg b) 6.69  1035 kg Observer

c) 9.69  1035 kg  min

d) 3.75  1035 kg
59. Which one of the following represent travelling wave

a) y  A  x  vt  b) y  ACos  ax  bt  c) y  A log  x  vt  d) y  f(x 2  vt 2 )

60. In a wave motion y = a Sin (kx – wt), y can represent

a) electric field b) magneticfield c) displacement d) pressure

61. The plane wave represented by an equation of the form y  f  x  vt  implies the propagation along
the positive x-axis with out change of shape with constant velocity V.

 dy   dy  dy 2  2 
2 d y dy 2 d2y dy 2 d2y
a)     V   b) 2   V  2 c)  V d) 
dt dx dt  dx  dt 2 dx 2 dt 2 dx 2

62. A wave y  A cos   t  kx passes through a medium. If V is the particle velocity and  is the particle
acceleration then,

a) y,V and  all are in the same phase b)y lags behind V by a phase angle of
2
3
c) a leads y by a phase angle of  d) d) v leads a by a phase angle of .
2
63. A sound wave propagates in a medium of Bull’k modulus B by means of compressions and rare
fractions. If Pc and Pr are the pressures at compression and rarefaction respectively, ‘a’ be the wave
amplitude and k be the angular wave number then.
a) Pc is maximum and Pr is minimum. b) Pc is minimum and Pr is maximum
c) the pressure amplitude is Bak
d) if the displacement wave is y= a sin   t  kx , the pressure wave at an instant
is represented as P= Pr cos  t  kx which leads displacement wave by a phase angle of  /2.
64. A plane progressive wave of frequency 25Hz amplitude 2.5  105 m and initial phase zero propagates
along negative x-direction with a velocity of 300 m/s
At any instant, the phase difference between the oscillations at two points 6m apart along the line is 
and the corresponding amplitude difference is A.
a) A = 0 b)  = 0 c) A = 2.5  10–5 m d)  = 

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2
65. A wave equation is represented by f  x, t   Ae  B x  vt  , where A=1m, B= 1m 2 and v  2 ms 1

a) The profile of wave at t = 0s and t = 1 s is

y(m)

f f 2
b)  2
t x t=0s
1
t=1s
2 2
¶ f ¶ f
c) 2
=+4 2
¶t ¶x –2 –1 D 1 2 3

d) Data insufficient to arrive at a conclusion

66. The displacement of a particle in a medium due to a wave travelling in the x-direction through the
medium is given by y  a sin(t  x) where t is in second,  and  are constants.

2
a) The frequency of the wave is  b) The time period of the wave is

2 
c) The wavelength of the wave is d) The velocity of the wave is
 
67. A wave is travelling along a string. At an instant shape of the string is as shown figure. At this instant A
is moving upwards. Which of the following statements are correct
a) The wave is travelling to the right
b) Displacement amplitude of the wave A is equal to the displcement of B at this instant
c) At this instant velocity of C is also directed upwards
d) Phase difference between A and C may be equal to  / 2 if x   / 4
68. A transverse wave is travelling on a string. The equation of the wave
a) is the general equation for displacementof a particle of the string at any instant ‘t’.
b) is the equation of the shape of the string at any instant t.
c) must have sinusoidal form
d) is an equation of displacement for the particle at any one end at a particular time ‘t’.
69. A transverse sinusoidal wave of amplitude a, wavelength  and frequency f is travelling on a stretched
1
string. The maximum speed of any point on the string is v, where v is the speed of propagation of the
10
wave. If a  10 3 m and v  10 ms 1 then  and f are given by
10 3
a)   2   10 2 m b)   103 m c) f  Hz d) f  103 Hz
2
70. The energy per unit area associated with a progressive sound wave will be doubled if then
a) the amplitude of the wave is doubled
b) the amplitude of the wave is increased by 50%
c) the amplitude of the wave is increased by 43%
d) the frequency of the wave is increased by 43%

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71. Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing
to give phenomenon of interference. If a1 and a2 be their respective amplitudes,  be frequency for
both, ‘v’ be the velocity for both and  is the phase difference between the two waves then,
a) the resultant intensity varies periodically with time and distance.
2
I min  a1  a 2 
b) the resultant intensity with  is obtained.
I max  a1  a 2 
c) both the waves must have bee4n travelling in the same direction and must be coherent.
d) I s  I1  I 2  2 I1I 2 cos() , where constuctive interference jis obtained for path differences that are
1
even multiple of  and destructive interference is obtained for path differences that are even
2
1
multiple of.
2
72. S1 and S2 are two sources of sound emitting sine waves. The two sources are in phase the waves
wavelength 2m 4m
a) 1 m will result in constructive interference
S1 S2
b) 0.67 will result in constructive interference F
c) 2 m will result in constructive interference
d) 4 m will result in constructive interference
EXERCISE - II
(Linked comprehension type questions)

Passage - I
A travelling wave on a long stretched string along the positve x-axis is given by y = 5mm
2
 t x 
 5s  5cm  . Using this equation answer the following questions.
e
1. The velocity of the wave is
a) 1 m/s b) 5m/s c) 1 cm/s d) 1 mm/s
3. At t = 0, x = 0, the displacement of the wave is
a) 0 b)  c) 5 mm d) 10 mn
2. The plot of the displacement function at x = 10 cm and t=0 is best indicated by

y y
5e4 mm
a) b)
10
x x
-5mm 10
y y
5mm 4mm
c) d)
x x
10 10

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Passage - II
Two wires 1 and 2 of the same cross sectional area A=10mm2 and the same length but made of
different materials are welded together and their ends are rigidly clamped between two walls, as
shown in figure. The respective young’s moduli and coefficient of linear exansions are
y1  10 9 N / m 2 , y 2  2  10 9 N / m 2

1  6  10 4 0 C,  2  3  10 4 0 C
If tempertature of system reduced by 200 C then
4. Find tension in each wire
a) 80 b) 10 N c) 120 N d) 140 N
5. Find the displacement of the joint
a) 0 b) 10 cm c) 5 cm d) 2 cm
6. Find the first overtone frequency of the system if joint is a node and mass per unit length of the wires
are 1  0.3kg / mt and  2  0.075 kg / m, l0  1 m
a) 20 Hz b) 40 Hz c) 60 Hz d) 100 Hz
Passage -III
Two particles A and B are perfoming SHM along x and y axis respectively with equal amplitude
and frequency of 2 cm and 1HZ respectiely. Equillirium positions of the particles A and B are at the
co-ordinates (3cm,0) and (0,4cm) respectively. At t=0, B is at its equilibrium position and moving
towards the orgin, while  0.4  B
A is nearest to the origin and moving away from the origin.
x  3, 0
7. Equation of motion of particle A can be written as : A
a) x = (2cm) cos 2 t b) x = (3cm)-(2cm) cos 2 t
c) x = (2cm) sin 2 t d) x = (3cm)-(2cm) sin 2 t
y
8. Equation of motion of particle B can be written as
a) y = (2cm)cos 2 t b) y = (4cm)-(2cm)cos 2 t
c) y = (2cm)sin 2 t d) y = (4cm)-(2cm)sin 2 t
9. Minimum and Maximum distance between A and B during the motion is
a) 5 cm and 61 cm b)3 cm and 7 cm c) 1 cm and 5 cm d) 9 cm and 16 cm

Passage -IV
As shown in the figure two sources producing sound SI and SII (velocity of sound 360 m/sec) each
producing sound of frequency 200 Hz. SI is rotating anti clock wise where as SII is approaching
observer O each with a speed 10 m/sec. (neglect radius of circular path of SI), then calculate
B

C
A SII
O

D
SI

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10. Range of number of beats received by observer O at rest is (nearly)

a) 0 to 5.6 b) 0 to 5 c) 1 to 4 d) 0 to 7.5
11. If O is approaching SI with a speed 10 m/sec. Number of beats received by ‘O’ per second when SI is at C.
a) 4 beats/sec b) 5.5 beats/sec
c) 3 beats/sec d) beats cannot be distinguished

12. If wind is blowing from right to left with a speed 10 m/sec and observer is at rest find the number of
beats received by observer when SI is at A. (nearly)
a) 5.5 b) 5 c) 4 d) 11
Passage -V
A Boat is travelling in a river with a speed 10 m/s along the stream flowing river through a rigid
support. The wave length of the sound emitted from the transmitter inside the water is 14.45 mm.
Assume that attenuation of sound in water and air is negligible (Temp of air & water = 200 C . Density
of river = 10 3 kg/m 3 , B = 2.088  10 9 Pa. R =8.31J/mole–K mean molecular wt of air =
28.8  10–3 kg / m3 and  of air = 1.4)
13. Velocity sound in water is
a) 1100 m/s b) 1445 m/s c) 1335 m/s d) 1220 m/s
14. Frequency of sound detected by the receiver at rest would be
a) 1.0069  105 Hz b) 1.1111  105 Hz c) 2.2220  105 Hz d) 1.321  105 Hz
15. Find frequency of sound detected by the receiver in air :
a) 1.0111  10 Hz c) 1.0550  10 Hz d) 2.1110  10 Hz
5 5 5
b) 1.0304  105 Hz
Passage - VI
As shown in the figure a vibrating tunning fork of frequency 512 Hz is moving towards the wall with
a speed 2m/s. Take speed ofsound v= 340 m/s and answer the following questions.

2 m/s

16. Suppose that a listner is located at rest between the tuning fork and the wall, Number of beats heard
by the listener per sec will be
a) 4 b) 3 c) 0 d) 1
17. If the listener, along with the source, is moving towards the wall with the same speed, i.e., 2 m/s, such
that the source remains between the listener and the wall, number of beats heard by the listener per sec
will be
a) 3 b) 8 c) 0 d) 6
18. If the listener, along with the source, is moving towards the wall with the same speed i.e., 2 m/s. such
that he (listener) remains between the source and the wall, number of beats heard by him will be
a) 2 b) 6 c) 8 d) 4

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EXERCISE - III
(Match the following type questions)
1. COLUMN I COLUMN II
A) A vertical rod is hit vertically p) pressure wave
B) A vertical rod is hit horizontally q) transverse wave
C) A cylindrical tube having a gas r) Displacement wave
is vibrated by a tuning fork
D) Ripples on water surface s) longitudinal wave
 
2. A wave disturbance in a medium is desiribed by Y  0.02 cos  50    cos x . Where x and y are in m
2
and t in sec. The values in column - II are in SI units.
COLUMN I COLUMN II
A) Node occurs at p) 0.3
B) Antinode occurs at q) 5.0
C) speed of wave r) 0.2
D) wave length s) 0.15
3. COLUMN I COLUMN II
A) Reflection in rigid surfaces p) f > 20,000 Hz
B) Ultra sonic waves q) phase change of  radians
C) Reflection at free boundary r) directon of propagation changes
D) Echo s) no phase change
4. Consider a situtation (i)

 x   x 
two sound waves y1  0.2 sin 504   t  and y 2  0.6 sin 490   t 
300 
 are superimposed
 300 
consider another situtation

 x   x 
(ii) two sound waves y1  0.2 sin 504  t  y 2  0.4 sin 504   t 
300   300  are superimposed
and

COLUMN I COLUMN II
A) In Situtaion - (i) p) Stationary waves are formed
B) In situtaion - (ii) q) There will be phenomenon of beats
C) When two waves of same frequency and r) Amplitude of reasultant wave very
amplitude are travelling in opposite periodically with position
directons superimpose
D) If the intensity of sound alternately s) Amplitude of the resultant wave will
increases and decreases periodically vary periodically with time
as a result of super position of waves
of slightly different frequencies

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LEVEL - II (LS) ANSWERS

EXERCISE - I
1) c 2) d 3) abcd 4) a 5) c 6) d 7) a 8) c 9) b 10) d

11) b 12) a 13) c 14) d 15) a 16) c 17) a 18) c 19) a 20) d

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

31) d 32) a 33) c 34) d 35) b,d 36) c 37) c 38) a 39) c 40) a

41) c 42) b 43) a 44) b 45) b 46) d 47) d 48) c 49) b 50) a

51) d 52) d 53) b 54) b 55) c 56) d 57) a 58) a 59) b 60) ad

61) ab 62) bcd 63) acd 64) ad 65) abc 66) bcd 67) bd 68) ab 69) ac 70) cd

71) abcd 72) abd

EXERCISE - II
01) c 02) c 03) b 04) c 05) a 06) b 07) b 08) d 09) a 10) a

11) b 12) a 13) b 14) a 15) b 16) c 17) d 18) b

EXERCISE - III
1) A - rs ; B - qr ; C - prs ; D - pr 2) A - s ; B - p ; C - q ; D - r
3) A - qr ; B - p ; C - rs ; D - qr 4) A - qrs ; B - pr ; C - pr ; D - qs

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