1. Which of the following expressions represents a simple harmonic progressive wave?
1) A sin ωt 2) A sin ωt cos kx 3) A sin (ωt - kx) 4) A cos kx
Ans: (3)
2. Which of the following expressions represents simple harmonic stationary wave?
1) A sin ωt + B cos ωt 2) A sin ωt + B cos kx
3) A sin ωt cos kx 4) A sin (ωt - kx)
Ans: (3)
3. If a stretched string fixed at both the ends has 'n' nodes then the length of the string is 
4. The rms velocity of the molecules of a gas is c and velocity of sound in the gas is v. The relation between v and c is
Ans: (4)
5. A cylindrical tube, open at both ends has a fundamental frequency 'f' in air, the tube is vertically dipped in water so that half of it is in water, the fundamental frequency of the air column is
Ans: (3)
6. The phenomenon of beats is
1) a characteristic property of light waves only
2) a characteristic property of sound waves only
3) a characteristic property of radiowaves only
4) a particular case of the phenomenon of interference
Ans: (4)
7. Echoes arise from
1) reflection 2) refraction
3) diffraction 4) dispersion
Ans: (1)
8. Match the following properties of a progressive wave in Column - I with the corresponding properties of the particles in Column - II.
| Column - I | Column - II |
| a) velocity | e) Amplitude |
| b) wavelength | f) period of oscillation |
| c) frequency | g) Elastic modulus |
| d) Intensity | h) frequency of oscillation |
1) a - h, b - e, c - g, d - f 2) a - g, b - f, c - e, d - h
3) a - g, b - h, c - f, d - e 4) a - f, b - e, c - g, d - h
Ans: (2)
Ans: (2)
10. A wave is expressed by the equation y = 0.5 sin {Π(0.01 x -5t} where y and x are in metres and 't' in seconds. The speed of propagation of the wave and wavelength are
1) 100 m/s, 50 m 2) 150 m/s, 100 m 3) 200 m/s, 150 m 4) 300 m/s, 200 m
Ans: (4)
11. A wire under a load has a frequency 20 Hz, when the load is completely immersed in water, its frequency is 10 Hz. The relative density of the material of the load is
Ans: (2)
12. The linear density of a string is 2 × 10-4 kg/ m. A transverse wave is propagating on the string and is described by the equation and y = 5 sin (30 t + 2x) where x and y are measured in meters and t is in seconds. The tension in the wire is
1) 0.12 N 2) 0.045 N 3) 0.45 N 4) 0.09 N
Ans: (2)
13. At what temperature is the velocity of sound in a gas is twice the velocity of sound in the same gas at 27°C?
1) 54°C 2) 627°C 3) 927°C 4) 327°C
Ans: (3)
14. 64 tuning forks are arranged such that each fork produces 4 beats per seond with next one. If the frequency of the last fork is one octave higher than the first, the frequency of the first tuning fork in 'Hz' is
1) 252 2) 256 3) 504 4) 36
Ans: (2)
15. A tuning fork produces 5 beats with Sonometer wires of 40 cm as well as 44 cm, other factors remaining constant, then frequency of the tuning fork is
1) 80 Hz 2) 88 Hz 3) 105 Hz 4) 160 Hz
Ans: (3)
16. Two factories are sounding their siren at 800 Hz, an observer goes from one factory to the other at a speed of 2 ms-1. The number of beats heard by the observer if the velocity of sound is 320 ms-1 is
1) 2 2) 4 3) 8 4) 10
Ans: (4)
17. A stone is dropped into a well of depth 45 m after how much time the splash is heard (speed of sound is 340 m/s and g = 10 m/s2)
1) 2.69 s 2) 3.13 s 3) 3.8 s 4) 4.13 s
Ans: (2)
18. 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?
1) 600 Hz 2) 680 Hz 3) 620 Hz 4) 660 Hz
Ans: (2)
19. A transverse wave of amplitude 0.5 m wavelength 1 m and frequency 2 Hz is propagating in a string in the negative X - direction. The equation of this wave is
1) y = 0.5 sin (2Πx - 4Πt) 2) y = 0.5 sin (2Πx + 4Πt)
3) y = 0.5 sin (Πx - 2Πt) 4) y = 0.5 sin (2Πx + 2Πt)
Ans: (2)
20. A Sonometer wire 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 is
1) 4 segments 2) 6 segments 3) 3 segments 4) 2 segments
Ans: (4)
21. 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
Ans: (3)
22. A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations simultaneously in the fundamental mode. The length of open pipe is now halved and of closed pipe is doubled. The number of beats produced
1) 8 2) 7 3) 4 4) 2
Ans: (2)
1) a - f, b - h, c - g, d - e 2) a - f, b - g, c - h, d - e
3) a - g, b - f, c - e, d - h 4) a - g, b - f, c - h, d - e
Ans: (2)
24. 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)
Ans: (1)
25. 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 36 km/ 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
Ans: (2)
Waves and Oscillations
1. A hollow sphere is filled with water. It is hung by a long thread to make it a simple pendulum. As the water flows out of a hole at the bottom of the sphere, the frequency of oscillation will
1) go on increasing 2) go on decreasing
3) first increases and then decreases
4) first decreases and then increases
2. The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the periodic motion as y = 8 sin2(t/2) sin (10t) is .....
1) 3 2) 4 3) 6 4) 8
3. A particle moves with a simple harmonic motion in a straight line. In the first second starting from rest it travels a distance a and in the next second it travels a distance b in the same direction. Then the amplitude of the motion is
1) 3a2/3b - a 2) 3a2/3a - b 3) 2a2/3a - b 4) 2a2/3b - a
4. A simple pendulum is making oscillations with its bob immersed in a liquid of density n times less than the density of the bob. What is its period?
5. The potential energy of a particle executing SHM along the X−axis is given by, U = U0 - U0 cosax. What is the period of oscillation?
6. A particle executing SHM of amplitude ‘a’ has a displacement a/2 at t = T/4 and a negative velocity. Then the epoch of the particle is
1) π/3 2) 2π/3 3) π 4) 5π/3
7. A particle executing SHM has velocities u and v and accelerations a and b in two of its positions. Then the distance between these two positions is
1) u2 - v2/a + b 2) v2 + u2/a - b 3) v2 + u2/a + b 4) v2 - u2/a - b
8. Two particles are executing identical SHM described by the equations, x1 = a cos (ωt + π/6) and x2 = a cos (ωt + π/3). Then the minimum interval of time between the particles crossing the respective mean positions is
1) π/2ω 2) π/3ω 3) π/4ω 4) π/6ω
9. The potential energy of a particle of mass 1kg in motion along the X - axis is given by: U = 4(1 -cos2x), where x is in meters. Then the period of small oscillation (in seconds) is
1) π 2) 2π 3) π/2 4) √2 π
10. A particle performs SHM with amplitude A and time period T. The mean velocity of the particle over the time interval during which it travels a distance of A/2 starting from extreme position is
1) A/T 2) 2A/T 3) 3A/T 4) A/2T
11. A particle performing SHM according to the equation x = 3 sin ( 2πt/18 + π/6), where ‘t’ is in seconds. Then the distance travelled by the particle in 39 s is
1) 24 cm 2) 25.5 cm 3) 1.5 cm 4) 15.5 cm
12. A horizontal spring-block system of mass 2 kg executes SHM. When the block is passing through its equilibrium position, an object of mass 1 kg is put on it and the two move together. The new amplitude of vibration is (A being its initial amplitude) 
13. The equation of a transverse wave travelling on a rope is given by y = 10 sinπ (0.01x - 2t) where y and x are in cm and t in seconds. Then the maximum transverse speed of a particle in the rope is
1) 63 cm/s 2) 75 cm/s 3) 10 cm/s 4) 55 cm/s
14. The path difference between the two waves 
15. A simple harmonic wave is represented by the equation y(x, t) = a0 sin2π (νt - x/λ). If the maximum particle velocity is three times the wave velocity, the wavelength λ is
1) πa0 2) πa0/2 3) πa0/3 4) 2πa0/3
16. The amplitude of a wave propagating in the positive y - direction is
1) 0.5 m/s 2) 1 m/s 3) 1.5 m/s 4) 2 m/s
17. A progressive wave in a stretched string has a speed of 100 cm/s, and frequency 100 Hz. The phase difference between two points 2.75 cm a part on the string, in radians, is
1) 0 2) π/4 3) 3π/8 4) 11π/2
18. At t = 0, a transverse wave pulse in a wire is described by y = 6/(x2 - 3) where x and y are in meters. The function y (x, t) describes this wave equation if it is travelling in the positive x - direction with a speed of 4.5 m/s is 
19. A string of length 2L, obeying hooke’s law, is stretched so that its extension is L. The speed of the transverse wave travelling on the string is V. If the string is further streteched so that the extension in the string becomes 4L. Then the speed of the transverse wave travelling on the string will be 
20. The intensity of a sound gets reduced by 20% on passing through a slab. Then the reduction in intensity on passage through two such consecutive slabs is
1) 30% 2) 40% 3) 36% 4) 46%
21. Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If the speed of sound is 340 m/s, what must be the value of u so that he hears 10 beats per second?
1) 2 m/s 2) 3 m/s 3) 3.5 m/s 4) 2.5 m/s
22. The frequency changes by 10% as the source approaches a stationary observer with a constant speed Vs. What should be the percentage change in frequency as the source recedes from the observer with the same speed? (Given that Vs << V, V being the velocity of sound in air)
1) 10% 2) 20% 3) 15% 4) 25%
23. The apparent frequency of the whistle of an engine changes in the ratio of 6 : 5 as the engine passes a stationary observer. If the velocity of sound is 330 m/s, then the velocity of the engine is
1) 0.33 m/s 2) 3 m/s 3) 30 m/s 4) 300 m/s
24. A source of sound emits 200 πW power which is uniformly distributed over a sphere of radius 10 m. What is the loudness of sound on the surface of the sphere?
1) 70 dB 2) 80 dB 3) 117 dB 4) 127 dB
25. A tuning fork of frequency 380 Hz is moving towards a wall with a velocity 4 m/s. Then the number of beats heard by a stationary listner between direct and reflected sounds will be (velocity of sound in air = 340 m/s)
1) 0 2) 5 3) 7 4) 10
26. A source emitting a sound of frequency f is placed at a large distance from an observer. The source starts moving towards the observer with a uniform acceleration ‘a’. If the speed of sound in medium is v, then the frequency heard by the observer corresponding to the wave emitted just after the source starts is
1) vf2/2vf - a 2) 2vf2/2vf + a 3) 2vf2/3vf - a 4) 2vf2/2vf - a
27. Spherical sound waves are emitted uniformly in all directions from a point source. The variation in sound level as a function of distance ‘r’ from the source can be expressed as
1) - b log ra 2) a - b(log r)2 3) a - b logr 4) a - b/r2
28. The equation of a stationary wave is y = 0.8 cos (πx/20) sin(200πt) where x is in cm and t is in s. Then the separation between consecutive nodes will be
1) 10 cm 2) 20 cm 3) 30 cm 4) 40 cm
29. The ratio of intensities between two coherent sound sources is 4 : 1. The difference of loudness in decibels (dB) between maximum and minimum intensities when they interfere in space is
1) 10 log 2 2) 10 log 3 3) 20 log 2 4) 20 log 3
30. A sound wave of wave length λ travels towards the right horizantally with a velocity v1. It strikes and reflects from a vertical plane surface, traveling at a speed v2 towards the left. then the number of positive crests striking in a time interval of 3s on the wall is
1) 3(v1 + v2)/λ 2) 3(v1 - v2)/λ 3) 3(v1 + v2)/3λ 4) 3(v1 - v2)/3λ
31. Two closed organ pipes, when sounded together produce 5 beats/s. If their lengths are in the ratio 100 : 101, then the fundamental notes (in Hz) produced by then are
1) 245, 250 2) 250, 255 3) 495, 500 4) 500, 505
32. Two organ pipes, both closed at one end, have lengths l and l + ∆l (neglect the end correction). If the velocity of sound in air is V, then the number of beats per second is
1) V/4l 2) V/2l 3) V/2l2. ∆l 4) V/2l2. ∆l
Answers: 1-4; 2-1; 3-3; 4-2; 5-3; 6-1; 7-1; 8-4; 9-3; 10-3; 11-2; 12-1; 13-1; 14-2; 15-4; 16-1; 17-4; 18-4; 19-4; 20-3; 21-4; 22-1; 23-3; 24-3; 25-1; 26-4; 27-3; 28-2; 29-4; 30-1; 31-4; 32-4.
