wave motion

WAVE MOTION

1. An astronaut can't hear his companion at the surface of the moon becausea) produced frequencies are above the radio frequenciesb) there is no medium for sound propagationc) temperature is too low during night and too high during dayd) there are too many craters on the surface of the moon.

2. Which of the following expressions is that of a simple harmonic progressive wavea) tsina ω b) )kxcos()t(sina ω c) )kxt(sina −ω d) kxcosa .

3. The displacement represented by y x t a kx t( , ) cos( )= +ω representsa) transverse wave propagating in +x direction b) transverse wave propagating in -x directionc) longitudinal wave propagating in +x direction d) longitudinal wave propagating in - x direction

4. A transverse wave is described by the equation Y = Y0 sin 2 π (ft - λπ / ). The maximum particle velocity is equal to four times the wave

velocity if °y is equal to

a) λf b) πλ /2 c) λf2 d) πλ /

5. The equation of a wave travelling in a string can be written as y = 3 cos π ( 100 t - x ). Its wavelength isa) 100 cm b) 2 cm c) 5 cm d) none of these

6. The equation of a transverse wave is given by y x t= −10 0 01 2sin ( . )π where y and x are in cm and t is in sec. Its frequency isa) 10 sec-1 b) 2 sec-1 c) 1 sec-1 d) 0.01 sec-1

7. The diagram shows the propagation of a wave. Which points are in phase

a) A and B b) B and C

c) B and D d) E and B

8. The sound carried by air from a sitar to a listener is a wave of the following typea) longitudinal stationary b) transverse progressive c) transverse stationary d) longitudinal progressive

9. Sound waves are travelling in a medium whose adiabatic elasticity is E and isothermal elasticity E'. The velocity of sound wave is proportionalto

a) E' b) E c) E ' d) E/E'

10. The temperature at which the speed of sound in air becomes double of its value at 27°C isa) 54°C b) 327°C c) 927°C d) -123°C

11. Velocity of sound is measured in hydrogen and oxygen gases at a given temperature. The ratio of two velocities will be (VH / V0 )a) 1 : 4 b) 4 : 1 c) 1 : 1 d) 32 : 1

12. If the amplitude of waves at a distance r from a line source is A, then the amplitude at a distance 4r will bea) 2A b) A c) A/2 d) A/4

13. A particle is oscillating according to the equation x = 7 cos 0.5 π t, where t is in seconds. The point moves from the position of equilibriumto maximum displacement in timea) 4.0 s b) 2.0 s c) 1.0 s d) 0.5 s

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14. The amplitude of a damped oscillator becomes half in 1 minute. The amplitude after 3 minutes will be 1/x times the original, where x isa) 2 × 3 b) 23 c) 3 2 d) 3 × 22

15. The distance between two points differing in phase by 60° on a wave having a wave velocity 360 metre/sec and frequency 500 Hz isa) 0.72 meter b) 0.18 meter c) 0.12 meter d) 0.36 meter

16. When a sound wave of frequency 300 Hz passes through a medium, the maximum displacement of a particle of the medium is 0.1 cm. Themaximum velocity of the particle is equal toa) 60 π cm/s b) 30 π cm/s c) 30 cm/s d) 60 cm/s

17. Two particles P and Q describe S.H.M. of same amplitude a, frequency v along the same straight line. The maximum distance between the

two particles is a 2. The initial phase difference between the particle isa) zero b) π /2 c) π /6 d) π /3

18. A sound wave travelling with a velocity v in a medium A reaches a point on the interface of medium A and medium B. If the velocity in themedium B be 2v, the angle of incidence for total internal reflection of the wave will bea) > 15° b) > 30° c) > 45° d) > 90°

19. The complete destructive interference of two sound waves takes place when the two waves are travelling in the same directiona) with the same frequency and amplitude and are in phase b) with the same frequency and amplitude and are in opposite phasec) with the same frequency and amplitude d) with the same frequency and opposite phase.

20. If the intensities of the interfering waves be I1 and I2, then the contrast between maximum and minimum intensity is good whena) I1 >> I2 b) I1 << I2 c) I1 = I2 d) either I1 or I2 is zero.

21. Two adjacent piano keys are struck simultaneously. The notes emitted by them have frequencies n1 and n2. The number of beats heard persecond isa) ( ) /n n1 2 2− b) ( ) /n n1 2 2+ c) n n1 2− d) 2 1 2( )n n−

22. If two tuning forks A and B are sounded together, they produce 4 beats per second. A is then slightly loaded with wax, they produce twobeats when sounded again. The frequency of A is 256. The frequency of B will bea) 250 b) 252 c) 260 d) 262

23. Two tuning forks of frequencies 256 and 258 vibrations / second are sounded together. Then the time interval between two consecutivemaxima heard by an observer isa) 2 second b) 0.5 second c) 250 second d) 252 second

24. Tuning fork A of frequency 258 cycles / sec gives 8 beats with a tuning fork B. When prongs of B are cut and again A and B are sounded,the number of beats heard remains same. The frequency of B in cycles / sec isa) 250 b) 264 c) 242 d) 258

25. 41 tuning forks are arranged so that every fork gives 5 beats with the next. The last fork has frequency that is double of the first. Thefrequency of first fork isa) 200 b) 400 c) 205 d) 210

26. Beats are produced by two progressive waves of equal amplitudes. Maximum loudness at the waxing is x times the loudness of each wave.The value of x is

a) 1 b) 2 c) 2 d) 4

27. Two sounding bodies producing progressive waves given by y t1 4 400= sin π and y t2 3 404= sin π are situatedvery near to the ears of a person who will hear

a) 2 beats per second with intensity ratio ( 4/3 ) between maxima and minima


b) 2 beats per second with intensity ratio ( 49/1 ) between maxima and minimac) 4 beats per second with intensity ratio ( 7/1 ) between maxima and minimad) 4 beats per second with intensity ratio ( 4/3 ) between maxima and minima

28. Stationary waves are formed whena) two waves of equal amplitude and equal frequency travel along the same path in opposite directionsb) two waves of equal wavelengths and amplitude travel along the same path with equal speeds in opposite directionsc) two waves of equal wavelengths and equal phase travel along the same path with same speedd) two waves of equal amplitude and speed travel along the same path in opposite directions.

29. The equation of stationary wave is given bya) y y kx t= 2 0 sin cosω b) y y k x vt= −0 sin ( )

c) y y k x tT

= −FHGIKJ0 2cos π

λ d) y y v T= 0

2sinλ

30. Phase difference between two particles of a medium lying between two consecutive nodes isa) zero b) π /4 c) π /2 d) π

31. The equation of stationary wave is given by y x t= 5 3 40cos( / ) sinπ π where y and x are given in centimeters and time t inseconds, then the amplitude of the progressive wave isa) 5 cm b) 2.5 cm c) 10 cm d) 3 cm

32. For the stationary wave y x t= 4 15 96sin( / ) cos( )π π the distance between a node and the next antinode isa) 7.5 b) 15 c) 22.5 d) 30

33. Two loudspeakers L1 and L2 driven by a common oscillator and amplifier are set up as shown in the figure. As the frequency of the oscillatorincreases from zero, the detector at D recorded a series of maximum and minimum signals.What is the frequency at which the first maximum is observed ? ( Speed of sound = 330 m/s ).

a) 165 Hz b) 330 Hz c) 495 Hzd) 660 Hz

34. A sonometer wire of density d and radius a is held between two bridges at a distance L apart. The wire has a tension T. The fundamentalfrequency of the wire will be

a) n laT d

=FHGIKJ

12

2πb) n l

Ta d

=FHGIKJ

12 2π c) n

lT da

=FHGIKJ

12 2π d) n

lT a d=

12

2( )π

35. In a long cylindrical tube, the water level is adjusted and the air column above it is made to vibrate in unison with a vibrating tuning fork keptat the open end. Maximum sound is heard when the air column lengths are equal to

(a)λ λ λ4 2

34

, , (b)λ

λλ

232

, , c)λ λ λ23252

, , d)λ λ λ43454

, ,

36. There are two open organ pipes of exactly the same length and material but different radii. Thena) wider pipe has lower frequency b) narrower pipe has lower frequencyc) both the pipes have same frequency d) It cannot be said based on given data


37. A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. Thefundamental frequency of the air column is nowa) f / 2 b) 3f / 4 c) f d) 2f.

38. Transverse waves are generated in two uniform wires A and B of same material by attaching their free ends to a vibrating source offrequency 200 Hz. The cross sectional area A is half that of B while the tension on A is twice that on B. The ratio of the wavelengths of thetransverse waves in A and B isa) 1 : 2 b) 2 : 1 c) 1 : 2 d) 2 : 1

39. A stretched string of 1 m length, fixed at both ends, having a mass of 5 × 10-4 kg is under a tension of 20 N. It is plucked at a point situatedat 25 cm from one end. The stretched string would vibrate with a frequency ofa) 400 Hz b) 100 Hz c) 200 Hz d) 256 Hz

40. A wire under tension vibrates with a fundamental frequency of 450 per second. What would be the fundamental frequency if the wire werehalf as long, having twice the diameter and under one fourth tension.a) 225 cps b) 190 cps c) 247 cps d) 174 cps

Answers

1. b 2. c 3. b 4. b 5. b 6. c7. d 8. d 9. b 10. c 11. b 12. c13. c 14. b 15. c 16. a 17. b 18. b19. b 20. c 21. c 22. b 23. b 24. a25. a 26. d 27. b 28. b 29. a 30. d31. b 32. a 33. b 34. b 35. d 36. c37. c 38. d 39. c 40. a


wave motion

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