Tuesday, 19th June 2018
19 June 2018

## Waves – Physics 13

1.The equation of a progressive wave is given by y = sin[π(t/5-x/9+π/6)]Then which of the following is correct?
(a)v= 5 cm
(b)λ= 18 cm
(c)a = 0.04 cm
(d)f = 50 Hz
2.The velocity of sound in any gas depends upon
(a)wave length of sound only
(b)density and elasticity of gas
(c)the intensity of sound waves only
(d)amplitude and frequency of sound
3.If the amplitude of sound is doubled and the frequency is reduced to one fourth, the intensity of sound at the same point will be
(a)increasing by a factor of 2
(b)decreasing by a factor of 2
(c)decreasing by a factor of 4
(d)unchanged
4.A 5.5 metre long string has a mass of 0.035kg. If the tension in the string is 77N, the speed of a wave on the string is
(a)110 ms-¹
(b)165 ms-¹
(c)77 ms-¹
(d)102 ms-¹
5.Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, a path difference of40 cm is equivalent to phase difference of 1.6 π.The frequency of this wave is(a)165 Hz
(b)150 Hz
(c)660 Hz
(d)330 Hz
6.The transverse wave represented by the equation y=4sin(π/6)sin (3x-15t) has
(a)amplitude =4
(b)wavelength =4(π/3)
(c)speed of propagation =5
(d)period (π/15)
7.A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has
(a)three nodes and three antinodes
(b)three nodes and four antinodes
(c)four nodes and three antinodes
(d)four nodes and four antinodes
8.Two trains move towards each other with the same speed. The speed of sound is 340 m/s. If the height of the tone of the whistle of one of them heard on the other changes 9/8 times, then the speed of each train should be
(a)20 m/s
(b)2 m/s
(c)200 m/s
(d)2000 m/s
9.With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the propagation direction are
(a)Energy, momentum, and mass
(b)Energy
(c)Energy and mass
(d)Energy and linear momentum
10.The frequency of sinusoidal wave ξ= 0.40 cos[2000 t + 0.80]would be
(a)1000 πHz
(b)2000 Hz
(c)20 Hz
(d)(1000/π)Hz

11.For production of beats the two sources must have
(a)different frequencies and same amplitude
(b)different frequencies
(c)different frequencies, same amplitude and same phase
(d)different frequencies and same phase
12.The temperature at which the speed of sound becomes double as was at27°C is
(a)273° C
(b)0° C
(c)927° C
(d)1027°C
13.A stretched string resonates with tuning fork frequency 512 Hz when length of the string is0.5 m. The length of the string required to vibrate resonantly with a tuning fork of frequency 256Hz would be
(a)0.25 m
(b)0.5 m
(c)1 m
(d)2 m
14.A standing wave is represented by y= Asin (100t)cos (0.01x), where y and A are in millimeter, t in seconds and x is in metre. Velocity of wave is
(a)10²+²m/s
(b)1 m/s
(c)10-4m/s
(d)not derivable from above data
15.Which of the following equations represent awave?
(a)y= A sin ωt
(b)y= A cos kx
(c)y= Asin (at– bx+ c)
(d)y= A (ωt –kx)
16.A wave of frequency 100 Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of10 cm from the fixed end of the string.The speeds of incident (and reflected) waves are
(a)5m/s
(b)10 m/s
(c)20 m/s
(d)40 m/s
17.From a wave equation: y=the frequency of the wave is
(a)5 Hz
(b)15 Hz
(c)20 Hz
(d)25 Hz
18.Two waves are approaching each other with a velocity of 20m/s and frequency n. The distance between two consecutive nodes is
(a)20n
(b)10n
(c)5n
(d)10n
19.Two waves are said to be coherent if they have
(a)same phase but different amplitude
(b)same frequency but different amplitude
(c)same frequency, phase & amplitude
(d)different frequency, phase and amplitude
20.The speed of a wave in a medium is 760 m/s. If3600 waves are passing through a point in the medium in 2 min, then their wavelength is
(a)13.8 m
(b)25.3 m
(c)41.5 m
(d)57.2 m
21.A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner is 4.2 MHz. The speed of sound in a tissue is 1.7 km/s. The wavelength of sound in tissue is close to
(a)4×10-4m
(b)8×10-4m
(c)4 x10-³m
(d)8×10-³m
22.A source of sound gives 5 beats per second, when sounded with another source of frequency 100/sec. The second harmonic of the source, together with a source of frequency 205/secgives 5 beats per second. What is the frequency of the source?
(a)95 sec-¹
(b)100 sec-¹
(c)105 sec-¹
(d)205 sec-¹
23.Two sound waves having a phase difference of60º have path difference of
(a)2λ
(b)/λ2
(c)λ/3
(d)λ/6
24.Astar, which is emitting radiation at a wavelength of 5000 Å, is approaching the earth with a velocity of 1.50 × 10³+³ m/s. The change in wavelength of the radiation as received on the earth is
(a)0.25 Å
(b)2.5 Å
(c)25 Å
(d)250 Å

25.What is the effect of humidity on sound waves when humidity increases?
(a)speed of sound waves is more
(b)speed of sound waves is less
(c)speed of sound waves remains same
(d)speed of sound waves becomes zero
26.Theequationofa soundwave is given as:y= 0.0015 sin (62.4 x+ 316 t). The wavelength of this wave is
(a)0.4 unit
(b)0.3 unit
(c)0.2 unit
(d)0.1 unit
27.Two waves of the same frequency and intensity superimposed each other in opposite phases.After the superposition, the intensity and frequency of waves will
(a)increase
(b)decrease
(c)remain constant
(d)become zero
28.An organ pipe P1closed at one end vibrating in its first overtone and another pipe P2, open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1and P2respectively are given by
(a)1 : 2
(b)1 : 3
(c)3 : 8
(d)3 : 4
29.The speed of a wave in a medium is 960 m/s. If3600 waves are passing through a point in the medium in 1 min., then the wavelength of the wave is
(a)8 m
(b)12 m
(c)16 m
(d)20 m
30.The equation of a travelling wave is y = 60cos (180t – 6x)where y is in microns, t in second and x in metres.The ratio of maximum particle velocity to velocityof wave propagation is
(a)3.6
(b)3.6×10–4
(c)3.6 ×10–6
(d)3.6×10–11
31.A cylindrical resonance tube open at both ends,  has a fundamental frequency, f, in air.If half of the length is dipped vertically in water, the fundamental frequency of the air column will be
(a)2f
(b)3f/2
(c)f
(d)f/2
32.A transverse wave is represented by the equation y=y0 sin (2π/λ)(vt-x) For what value of  λ is the maximum particle velocity equal to two times the wave velocity?
(a)λ=2πyo
(b)λ=πyo/3
(c)λ=πyo/2
(d)λ=πyo
33.A vehicle, with a horn of frequency n is moving with a velocity of 30 m/s in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency n+ n1.Then (if the sound velocity in air is 300 m/s)
(a)n1= 10n
(b)n1= 0
(c)n1= 0.1n
(d)n1= –0.1n
34.A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance1.21 Å between them. The wavelength of the standing wave is
(a)1.21 Å
(b)2.42 Å
(c)6.05 Å
(d)3.63 Å35.In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacements is 0.170 sec.The frequency of the wave is(a)1.47 Hz
(b)0.36 Hz
(c)0.73 Hz
(d)2.94 Hz
36.Resonance is an example of
(a)tuning fork
(b)forced vibration
(c)free vibration
(d)damped vibration
37.Two waves of lengths50 cm and 51 cm produce12 beats per sec. The velocity of sound is
(a)306 m/s
(b)331 m/s
(c)340 m/s
(d)360 m/s
38.If n1, n2and n3are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by
(a)n = n1+ n2+ n3
(b)1/n=1/n1+1/n2+1/n3
(c)1/√n=1/√n1+1/√n2+1/√n3
(d)√n=√n1+√n2+√n3

39.Two sound sources emitting sound each of wavelength are fixed at a given distance apart.A listener moves with a velocity u along the line joining the two sources. The number of beats heard by him per second is
(a)u/2λ
(b)2u/λ
(c)u/λ
(d)u/3λ
40.The equation of a wave is represented by :y=10-4  sin [100t-x/10]. The velocity of the wave will be
(a)100 m/s
(b)250 m/s
(c)750 m/s
(d)1000 m/s
41.A source and an observer move away from each other, with a velocity of 10m/s with respect to ground. If the observer finds the frequency of sound coming from the source as 1950 Hz, the noriginal frequency of source is(velocity of sound in air = 340 m/s)
(a)1950 Hz
(b)2068 Hz
(c)2132 Hz
(d)2486 Hz
42.A string of 7 m length has a mass of 0.035 kg. If tension in the string is 60.5 N, then speed of a wave on the string is
(a)77 m/s
(b)102 m/s
(c)110 m/s
(d)165 m/s
43.The equation for transverse wave travelling along the positive x-axis with amplitude 0.2 m, velocity v=360 ms–1and wavelength = 60 m can be written as
(a)y=0.2sin[2π(6t-x/60)] (b)y=0.2sin[π(6t+x/60)] (c)y=0.2sin[2π(6t-x/60)] (d)y=0.2sin[2π(6t+x/60)] 44.A whistle of frequency 385 Hz rotates in a horizontal circle of radius 50 cm at an angular speed of 20 radians s-¹. The lowest frequency heard by a listener a long distance away at rest with respect to the centre of the circle, given velocity of sound equal to 340 ms-¹, is
(a)396 Hz
(b)363 Hz
(c)374 Hz
(d)385 Hz
45.An observer moves towards a stationary source of sound with a speed 1/5th of the speed of sound. The wavelength and frequency of the sound emitted are λ  and f respectively.The apparent frequency and wavelength recorded by the observer are respectively.
(a)0.8f, 0.8 λ
(b)1.2f, 1.2 λ
(c)1.2f,  λ
(d)f, 1.2 λ
46.A car is moving towards a high cliff. The car driver sounds a horn of frequency f. There reflected sound heard by the driver has frequency 2f. If v be the velocity of sound, then the velocity of the car, in the same velocity units, will be
(a)v/2
(b)v /√2
(c)v/3
(d)v/4
47.The phase difference between two waves,represented by y1= 10–6sin{100 t+ (x/50) + 0.5} my2= 10–6cos{100 t+ (x/50)}mwhere x is expressed in metres and tis expressed in seconds, is approximately
48.Two vibrating tuning forks produce progressive waves given by y1= 4 sin500 πtand y2= 2 sin 506 πt. Number of beats produced per minute is
(a)360
(b)180
(c)60
(d)3
49.A point source emits sound equally in all directions in a non–absorbing medium. Two points Pand Qare at distances of 2 mand 3mrespectively from the source. The ratio of the intensities of the waves at PandQis
(a)3: 2
(b)2 : 3
(c)9: 4
(d)4:9

1. Ans(2)
2. Ans(2)
3. Ans(3)
4. Ans(1)
5. Ans(3)
6. Ans(3)
7. Ans(4)
8. Ans(1)
9. Ans(2)
10. Ans(4)
11. Ans(2)
12. Ans(3)
13. Ans(4)
14. Ans(1)
15. Ans(3)
16. Ans(3)
17. Ans(3)
18. Ans(2)
19. Ans(3)
20. Ans(2)
21. Ans(1)
22. Ans(3)
23. Ans(4)
24. Ans(3)
25. Ans(1)
26. Ans(4)
27. Ans(3)
28. Ans(3)
29. Ans(3)
30. Ans(2)
31. Ans(3)
32. Ans(4)
33. Ans(2)
34. Ans(1)
35. Ans(1)
36. Ans(2)
37. Ans(1)
38. Ans(2)
39. Ans(2)
40. Ans(4)
41. Ans(2)
42. Ans(3)
43. Ans(1)
44. Ans(3)
45. Ans(3)
46. Ans(3)
47. Ans(2)
48. Ans(2)
49. Ans(3)