Wave Dpp PDF

Exercise - I WAVE AND ITS CHARACTERISTICS 9. The equation of progressive wave is 1. Water waves are of the nature :   t x   (1) Transverse Y = 4sin   −  +  whe...

Exercise - I WAVE AND ITS CHARACTERISTICS 9. The equation of progressive wave is 1. Water waves are of the nature :   t x   (1) Transverse Y = 4sin   −  +  where x and y are  5 9 6 (2) Longitudinal in cm. Which of the following statement is (3) Sometimes longitudinal and sometimes true? transverse and longitudinal both (4) Neither transverse nor longitudinal (1)  = 18 cm 2. Sound wave are not polarized because : (2) amplitude = 0.04 cm (1) Their speed is less (3) velocity v = 50 cm/s (2) A medium is needed for their propagation (4) frequency f = 20 Hz (3) These are longitudinal 10. A plane progressive wave is represented by (4) Their speed depends on temperature the equation y = 0.25 cos (2t – 2x). 3. A thunder tap is heard 5.5 second after the The equation of a wave is with double the lightening flash. The distance of the flash is amplitude and half frequency but travelling in (velocity of sound in air is 330 m/sec.): - the opposite direction will be. (1) 3560 m (2) 300 m (1) y = 0.5 cos (t – x) (3) 1780 m (4) 1815 m (2) y = 0.5 cos (2t + 2x) 4. Transverse waves can propagate (3) y = 0.25 cos (t + 2x) (1) only in solids (4) y = 0.5 cos (t + x) (2) both in solids and gases 11. A plane wave is described by the equation (3) neither in solids nor in gases y = 3 cos  x − 10t −  . The maximum velocity (4) only in gases 4 2 5. Transverse elastic waves can be propagate in of the particles of the medium due to this wave is (1) Both solid & gas 3 (2) In solid but not gas (1) 30 (2) (3) 3/4 (4) 40 2 (3) Neither solid nor gas 12. The equation y = 4 + 2 sin (6t – 3x) represents (4) None a wave motion with 6. A wave of frequency 500 Hz travels between (1) amplitude 6 units X and Y and travel a distance of 600 m in 2 sec. (2) amplitude 4 units between X and Y. How many wavelength are (3) wave speed 2 units there in distance XY : (4) wave speed 1/2 units (1) 1000 (2) 300 (3) 180 (4) 2000 13. Due to propagation of longitudinal wave in a 7. If at a place the speed of a sound wave of medium, the following quantities also frequency 300 Hz is V, the speed of another propagate in the same direction : wave of frequency 150 Hz at the same place (1) Energy, Momentum and Mass will be: (2) Energy (1) V (2) V/2 (3) 2V (4) 4V (3) Energy and Mass 8. The equation of a progressive wave for a wire (4) Energy and Linear Momentum  x  14. The waves in which the particles of the is: Y = 4sin   8t −  . If x and y are 2  8  medium vibrate in a direction perpendicular measured in cm then velocity of wave is : to the direction of wave motion is known as : (1) 64 cm/s along – x direction (1) transverse waves (2) 32 cm/s along – x direction (2) propagated waves (3) 32 cm/s along + x direction (3) longitudinal waves (4) 64 cm/s along + x direction (4) stationary waves 15. Two wave are represented by equation PROGRESSIVE WAVE ON STRING y1 = a sin t y2 = a cos t 19. In a string the speed of wave is 10 m/s and its frequency is 100 Hz. The value of the phase the first wave – difference at a distance 2.5 cm will be : (1) leads the second by  (1) /2 (2) /8 (3) 3/2 (4) 2 (2) lags the second by  20. A uniform rope of mass 0.1 kg and length 2.5  m hangs from ceiling. The speed of transverse (3) leads the second by wave in the rope at upper end and at a point 2 0.5 m distance from lower end will be :  (1) 5 m/s, 2.24 m/s (2) 10 m/s, 3.23 m/s (4) lags the second by 2 (3) 7.5 m/s, 1.2 m/s (4) 2.25 m/s, 5 m/s 16. The distance between two consecutive crests 21. The equation of a wave on a string of linear in a wave train produced in string is 5 m. If density 0.04 kg m–1 is given by two complete waves pass through any point   t x  y = 0.02(m)sin 2  − . per second, the velocity of wave is   0.04(s) 0.50(m)   (1) 2.5 m/s (2) 5 m/s The tension in the string is : (3) 10 m/s (4) 15 m/s (1) 6.25 N (2) 4.0 N (3) 12.5 N (4) 0.5 N 22. The mathematical forms for three sinusoidal 17. The graph between wave number ( ) and travelling waves are given by angular frequency () is : Wave 1 : y(x,t) = (2cm) sin(3x–6t) Wave 2 : y(x,t) = (3cm) sin(4x–12t) frequency () Wave 3 : y(x,t) = (4cm) sin(5x–11t) Angular where x is in meters and t is in seconds. Of (1) these waves : (1) wave 1 has the greatest wave speed and Wave no. () the greatest maximum transverse string speed. frequency () (2) wave 2 has the greatest wave speed and Angular wave 1 has the greatest maximum (2) transverse string speed. (3) wave 3 has the greatest wave speed and Wave no. () the greatest maximum transverse string speed. frequency () (4) wave 2 has the greatest wave speed and Angular wave 3 has the greatest maximum (3) transverse string speed. 23. The figure shows an instantaneous profile of Wave no. () a rope carrying a progressive wave moving from left to right, then frequency () y Angular (4) A x Wave no. () B 18. The waves produced by a motorboat sailing on water are (a) the phase at A is greater than the phase at B (1) Transverse (b) the phase at B is greater than the phase at A (c) A is moving upwards (2) Longitudinal (d) B is moving upwards (3) Longitudinal and Transverse (1) a & c (2) a & d (3) b & c (4) b & d 24. Linear density of a string is 1.3 × 10–4 kg/m 31. Newton's formula for the velocity of sound in and wave equation is y = 0.021sin(x + 30t). gases is : Find the tension in the string where x in 2p p meter, t in sec. (1) v = (2) v =   (1) 1.17 × 10–2 N (2) 1.17 × 10–1 N (3) 1.17 × 10–3 N (4) None  3 p (3) v = (4) v = SOUND WAVES AND ITS CHARACTERISTICS p 2  25. The speed of sound in air at constant 32. Intensity level of a sound of intensity I is temperature 30 dB. The ratio I/I0 is (I0 is the threshold of (1) is proportional to the atmospheric hearing) pressure. (1) 1000 (2) 3000 (3) 300 (4) 30 (2) is proportional to the square of 33. If m is the velocity of sound in moist air and atmospheric pressure. d is the velocity of sound in dry air then : (3) is proportional to the square root of (1) m < d (2) m > d atmospheric pressure (3) d >> m (4) m = d (4) does not depend on atmospheric pressure. 34. A sine wave has an amplitude A and 26. At the room temperature the velocity of wavelength  Let V be wave velocity and v be sound in O2 gas is V. Then in mixture of H2 the maximum velocity of a particle in medium and O2 gas the speed of sound at same then. temperature:  (1) will be less than V (2) will be more than V (1) V = if A = 2 (3) will be equal to V (4) nothing can be said (2) V can not be equal to 27. The velocity of sound in a gas depends 3A (1) only on its wave length (3) V = if  = 2 (2) on the density and the elasticity of gas (4) V= if A = 2  (3) on intensity of the sound 35. A sings with a frequency (n) and B sings with (4) on the amplitude and the frequency. a frequency 1/8 that of A. If the energy 28. If at some point the amplitude of the sound remains the same and the amplitude of A is a, becomes double and the frequency becomes then amplitude of B will be : one fourth then at that point the intensity of (1) 2a (2) 8a (3) 4a (4) a sound will be :- 36. The velocities of sound at the same pressure (1) Become double (2) Be half in two monoatomic gases of densities 1 and (3) Become one fourth (4) Remain unchanged 2 are v1 and v2 respectively. If 1 = 4 , then the 29. A sound is produced in water and moves 2 towards surface of water and some sound v1 value of is : moves in air velocity of sound in water is v2 1450 m/s and that in air is 330 m/s. When 1 1 sound moves from water to air then the effect (1) (2) (3) 2 (4) 4 4 2 on frequency f and wave length  will be: 37. The time period of SHM of a particle is 12 s. (1) f and  will remain same The phase difference between the position at (2) f will remain same but  will increase t = 3s and t = 4s will be : (3) f will remain same but  will decrease (1) /4 (2) 3/5 (3) /6 (4) /2 (4) f will increase and  will decrease 38. Velocity of sound in medium is V. If the 30. When sound wave travels from air to water, density of the medium is doubled, what will which are of the following remain constant : be the new velocity of sound? (1) wavelength (2) velocity (3) frequency (4) intensity (1) 2V (2) V (3) V 2 (4) 2V  REFLECTION OF WAVES AND ECHO 46. Intensities ratio of two waves are 9:1 then the 39. A man standing on a cliff claps his hand and ratio of their maximum and minimum hears its echo after one second. If the sound intensities will be:- in reflected from another mountain then the (1) 10 : 8 (2) 7 : 2 (3) 4 : 1 (4)2 : 1 distance between the man & reflection points 47. When two tuning forks are sounded together is Vsound = 340 m/sec. x beats/sec are heard and frequency of A is n. (1) 680 m (2) 340 m Now when one prong of B is loaded with a little wax, the number of beats per second (3) 170 m (4) 85 m decreases. The frequency of fork B is : PRINCIPLE OF SUPERPOSITION OF WAVES : (1) n + x (2) n – x INTERFERENCE, BEATS (3) n – x2 (4) n – 2x 40. At a particle two simple harmonic motion are 48. A source x of unknown frequency produces acting along the same direction. These are 8 beats with a source of 250 Hz and 12 beats y1 = a1sin t and y2 = a2sin (t+). The with a source of 270 Hz. The frequency of resultant motion is also a simple harmonic source x is: motion whose amplitude will be: (1) 258 Hz (2) 242 Hz (1) a12 + a22 + 2a1a2cos (3) 262 Hz (4) 282 Hz 49. Two waves of wave length 2 m and 2.02 m (2) a12 + a22 + 2a1a2cos respectively moving with the same velocity and superimpose to produce 2 beats per sec. (3) a12 + a22 − 2a1a2cos The velocity of the waves is: (4) a12 + a22 − 2a1a2cos (1) 400.0 m/s (2) 402 m/s (3) 404 m/s (4) 406 m/s 41. The energy in the superposition of waves: - 50. A tuning fork produces 4 beats/sec. with (1) Is lost another tuning fork B of frequency 288 Hz. If (2) Increase fork is loaded with little wax no. of beats per (3) remain same, only redistribution occurs sec decreases. The frequency of the fork A, (4) None of the above before loading is 42. Waves from two sources superimpose on (1) 290 Hz (2) 288 Hz each other at a particular point. Amplitude (3) 292 Hz (4) 284 Hz and frequency of both the waves are equal. 51. Column-I Column-II The ratio of intensities when both waves A Longitudinal P Particles of the reach in the same phase and they reach with waves medium vibrate the phase difference of 90° will be perpendicular to the (1) 1:1 (2) 2 :1 (3) 2:1 (4) 4:1 wave propagation. 43. Two waves whose intensity are same (I) B Transverse Q Two progressive move towards a point P in same phase, then waves waves of slightly the resultant intensity at point P will be: different frequencies (1) 4 I (2) 2 I (3) 2 I (4) None superimpose in the 44. Ratio of amplitudes of two waves is 3:4. The same direction ratio of maximum and minimum intensity C Beats R Two progressive waves of same obtained from them will be : frequency (1) 7:1 (2) 49:1 (3) 1:25 (4) 5:1 superimpose in the 45. Two coherent sources of intensities I1 and I2 opposite directions produce an interference pattern, the D Stationary S Particles of the maximum intensity in the interference waves medium vibrate pattern will be – along the wave (1) I1 + I2 (2) I12 + I22 propagation. ( ) 2 (3) (I1+I2)2 (4) I1 + I2 (1) A-Q, B-R, C-Q, D-P (2) A-S, B-P, C-Q, D-R (3) A-Q, B-S, C-P, D-R (4) A-P, B-Q, C-S, D-R 52. What is the path difference for destructive STATIONARY WAVES OR STANDING interference? WAVES IN STRINGS (1) n (2) n( + 1) 59. A uniform string of length L and mass M is (n + 1) (2n + 1) fixed at both ends under tension T, then it can (3) (4) vibrate with frequency given by the formula. 2 2 53. When beats are produced by two progressive (1) f = 1T (2) f = 1 T waves of the same amplitude and of nearly 2 ML 2L M the same frequency, the ratio of maximum (3) f = 1 T (4) f = 1 M intensity to the intensity of one of the waves 2 M 2 LT will be n. Where n is 60. The speed of transverse waves in a stretched (1) 3 (2) 1 (3) 4 (4) 2 string is 700 cm/s. If the string is 2 m long, the frequency with which it resonates in 54. What is the beat frequency produced when fundamental mode is: following two waves are sounded together? (1) (7/2) Hz (2) (7/4) Hz x1 = 10 sin (404t – 5x), (3) (14) Hz (4) (2/7) Hz x2 = 10 sin (400t – 5x). 61. A wave represented by the equation (1) 4 (2) 1 (3) 3 (4) 2 y = acos(t–kx) is superposed by another 55. Two waves having equation wave to form a stationary wave such that x1 = a sin(t +1) x2 = a sin(t +2) the point x = 0 is a node. The equation for If in the resultant wave the frequency and other wave is – amplitude remains equals to amplitude of (1) y = a sin(t+kx) (2) y = – a cos(t–kx) superimposing waves. Then phase diff. (3) y = – a cos(t+kx) (4) y = – a sin(t–kx) between them – 62. A stretched string is vibrating according to (1)  (2) 2 (3) 3 (4)  the equation y = 5sin  x  cos 4t , where y 6 3 4 4  2  56. Two sources have frequency 256 Hz and and a are in cm and t is in sec. The distance between two consecutive nodes on the 258 Hz, then time difference between two strings is :- consecutive maxima is – (1) 2 cm (2) 4 cm (1) 1 s (2) 0·5 s (3) 8 cm (4) 16 cm (3) 2 ms (4) None 63. A wave of frequency 100 Hz travels along a 57. Two vibrating tuning forks produce string towards its fixed end. When this wave progressive waves given by Y1 = 4 sin 500t travels back, after reflection, a node is formed and Y2 = 2 sin 506 t. Number of beats at a distance of 10 cm from the fixed end. The produced per minute is: speed of the wave (incident and reflected) is : (1) 3 (2) 360 (3) 180 (4) 60 (1) 5 m/s (2) 10 m/s 58. Two plane progressive waves shows (3) 20 m/s (4) 40 m/s destructive interference at point P. Which of 64. Stationary wave is represented by the following statement is true at point P :- Y = A sin (100 t) cos (0.01 x) where y and A (1) Crest of one wave is superimposed on are in mm, t in sec and x in m. The velocity of the wave: crest of another wave (1) 1 m/s (2) 102 m/s (2) Trough of one wave is superimposed on (3) 10 m/s 4 (4) zero crest of another wave 65. If the tension in a sonometer wire is increased (3) Intensity of resultant wave is equal to the by a factor of four then fundamental intensity difference of two waves frequency of vibration changes by a factor of : (4) Resultant amplitude is equal to the (1) 4 (2) (1/4) amplitude sum of two waves (3) 2 (4) (1/2) 66. A sonometer wire, with a suspended mass of (1) increases (2) constant M = 1 kg., is in resonance with a given tuning (3) decrease (4) can't say fork. The apparatus is taken to moon where 73. A second harmonic has to generated in a the acceleration due to gravity is 1/6 that of string of length  stretched between two rigid earth. To obtain resonance on the moon, the supports. The points where the string has to value of M should be be plucked and touched are – (1) 1 kg. (2) 6 kg 3 (3) 6 kg (4) 36 kg (1) Pluck at touch at 2 4 67. Stationary waves are produced in 10m long stretched string. If the string vibrates in 5 (2) Pluck at touch at 2 4 segments and wave velocity is 20m/sec, then 3 the frequency is- (3) Pluck at touch at 4 4 (1) 10 Hz (2) 5 Hz (3) 4 Hz (4) 2Hz (4) Pluck at touch at 4 2 68. A standing wave having 3 nodes and 2 74. If the tension and diameter of a sonometer antinodes is formed between 1.21 Å distance wire of fundamental frequency (n) is doubled then the wavelength is and density is halved then its fundamental (1) 1.21 Å (2) 2.42 Å frequency will become: - (3) 0.605 Å (4) 4.84 Å n 69. A string under a tension of 129.6 N produces (1) (2) 2n 4 10 beats/sec when it is vibrated along with a n tuning fork. When the tension is the string is (3) n (4) 2 increased to 160 N it sounds in unison with same tuning fork. Calculate fundamental freq. 75. The tension in a piano wire is 10N. What should be the tension in the wire to produce of tuning fork. a note of double the frequency? (1) 100 Hz (2) 50 Hz (1) 10N (2) 20N (3) 150 Hz (4) 200 Hz (3) 40N (4) 80N 70. If vibrations of a string are to be increased to 76. Fundamental frequency of sonometer wire is n. a factor of two, then tension in the string must be made : If the length, tension and diameter of wire are (1) half (2) thrice tripled, the new fundamental frequency is: - (3) four times (4) eight times (1) n 3 (2) n/3 71. Stationary waves are so called because in (3) n 3 (4) n 3 3 them – 77. A string in a musical instrument is 50 cm long (1) The particles of the medium are not and its fundamental frequency is 800 Hz. If a disturbed at all frequency of 1000 Hz is to be produced, then (2) The particles of the medium do not required length of string is: - execute S.H. M. (1) 62.5 cm (2) 50 cm (3) There occurs no flow of energy along the (3) 40 cm (4) 37.5 wave 78. Four wires of identical lengths, diameters and (4) The interference effect can't be observed 72. In a sonometer wire, the tension is of the same material are stretched on a maintained by suspending a mass M from free sonometer wire. The ratio of their tension is end of wire. The fundamental frequency of 1 : 4 : 9 : 16. The ratio of their fundamental the wire is N Hz. If the suspended mass is frequencies is completely immerged in water the (1) 1 : 2 : 3 : 4 (2) 16 : 9 : 4 : 1 79. Given equation is related to 87. Velocity of sound in air is 320 m/s. A pipe y = cos  2 x  cos(2t) closed at one end has a length of 1 m    neglecting end corrections, the air column in (1) Transverse progressive the pipe can resonant for sound of frequency. (2) Longitudinal progressive (a) 80 Hz (b) 240 Hz (3) Longitudinal stationary wave (c) 500 Hz (d) 400 Hz (4) Transverse stationary wave (1) a (2) a,b (3) a,b,d (4) a,d 80. A stretched string is 1 m long. Its mass per 88. The velocity of sound in air is 330 m/s. The unit length is 0.5 g/m. It is stretched with a fundamental frequency of an organ pipe open force of 20 N. It plucked at a distance of 25 cm at both ends and of length 0.3 metre will be: from one end. The frequency of note emitted (1) 200 Hz (2) 550 Hz by it will be: (3) 300 Hz (4) 275 Hz (1) 400 Hz (2) 300 Hz 89. An air column having one end closed contains (3) 200 Hz (4) 100 Hz minimum resonance length 50 cm. If it is STATIONARY WAVE IN ORGAN PIPES 81. With the increase of temperature, the vibrated by same tuning fork then its next frequency of the organ pipe- resonance length will be – (1) increases (2) decreases (1) 250 cm (2) 200 cm (3) remains unchanged (4) can not say (3) 150 cm (4) 100 cm 82. An empty vessel is partially filled with water 90. If the air column in a pipe which is closed at the frequency of vibration of air column in the one end, is in resonance with a vibrating vessel tuning fork of frequency 260 Hz, then the (1) decreases length of the air column is : (vsound = 330 m/s) (2) increases (1) 35.7 cm (2) 31.7 cm (3) depends on the purity of water (3) 12.5 cm (4) 62.5 cm (4) remains the same 91. A sound wave of frequency 330Hz is incident 83. The end correction of resonance tube is 1 cm. normally at reflected wall then minimum If lowest resonant length is 15 cm then next distance from wall at which particle vibrate resonant length will be: - very much: - (Vsound = 330 m/s) (1) 36 cm (2) 45 cm (1) 0.25 m (2) 0.125 m (3) 46 cm (4) 47 cm (3) 1 m (4) 0.5 m 84. If the fundamental frequency for a COP is n, 92. An open organ pipe of length 33 cm, vibrates then the next three overtones will have ratio: - with frequency 1000 Hz. If velocity of sound (1) 2 : 3 : 4 (2) 3 : 4 : 5 is 330 m/s, then its frequency is: - (3) 3 : 7 : 11 (4) 3 : 5 : 7 (1) Fundamental frequency 85. A tube closed at one end and containing air produces, when excited, the fundamental (2) First overtone of pipe note of frequency 512 Hz. If the tube is open (3) Second overtone at both ends, the fundamental frequency that (4) Fourth overtone can be excited is (in Hz) 93. If V is the speed of sound in air then the (1) 1024 (2) 512 (3) 256 (4) 128 shortest length of the closed pipe which 86. An air column in pipe, which is closed at one resonates to a frequency n : end will be in resonance with a vibrating V V (1) (2) tuning fork of frequency 264 Hz if the length 2n 4n of the column in cm is : [v = 330 m/s] 4n 2n (1) 31.25 (2) 62.50 (3) 110 (4) 125 (3) (4) V V 94. The lengths of two closed organ pipes are DOPPLER EFFECT IN SOUND AND LIGHT WAVES 0.750 m and 0.770 m. If they are sounded 101. The apparent change in the pitch of sound together, 3 beats per second are produced. due to relative motion between observer and The velocity of sound will be :- the source is called: (1) 350.5 m/sec (2) 335.5 m/sec (1) Doppler's effect (3) 346.5 m/sec (4) None of these (2) Resonance of waves 95. What is minimum length of a tube, open at (3) interference both ends, that resonates with tuning fork of (4) none of the above frequency 350 Hz? (velocity of sound in 102. A siren blown in workshop emits waves of air = 350 m/s) frequency 1000 Hz. A car driver approaches (1) 50 cm (2) 100 cm the workshop with velocity 90 km/hour then (3) 75 cm (4) 25 cm frequency of sound heard by driver will be 96. An underwater sonar source operating at a in Hz. (Vsound = 330 m/s) frequency of 60 kHz directs its beam towards (1) 926 (2) 1076 the surface. If velocity of sound in air is (3) 1176 (4) 1000 330 m/s, wavelength and frequency of the 103. A star is continuously moving away from us waves in air are: - than the wavelength coming from star on the (1) 5.5 mm, 60 kHz (2) 3.30 m, 60kHz earth: - (3) 5.5 mm, 30 kHz (4) 5.5 mm, 80 kHz (1) Will shift towards violet colour 97. An organ pipe closed at one end has (2) Will shift towards red colour. fundamental frequency of 1500 Hz. The (3) remain unchanged (4) Will shift sometimes towards violet and maximum number of overtones generated by some other time it will shift towards red this pipe which a normal person can hear is colour. (1) 14 (2) 13 (3) 6 (4) 9 104. Doppler's effect in the form of frequency 98. Length of the close organ pipe is 1 m. At doesn't depend upon : which frequency resonance will not occur (1) Frequency produced by waves (v = 320 m/sec.) (2) Velocity of source (1) 80 Hz (2) 240 Hz (3) Velocity of observer. (3) 300 Hz (4) 400 Hz 99. An open resonating tube has fundamental (4) Separation between source & observer. frequency of n. When half of its length is 105. The term "Red shift" referring to doppler's dipped into water, then its fundamental effect for light represent which of following frequency will be: property: (1) n (2) n/2 (1) decrease in frequency (3) 2n (4) 3/2 n. (2) increase in frequency 100. A pipe is closed from one end and open from (3) decrease in intensity another end then which statement is true? (4) Increase in intensity (1) Node is formed slightly above the open 106. A source and an observer moves away from end. each other, with a velocity of 15 m/sec with (2) Node is formed slightly below the open respect to ground. If observer finds the end. frequency of sound coming from source as (3) Antinode is formed slightly above the 1950 Hz. Then actual frequency of source will open end. be (velocity of sound = 340 m/sec.) : (4) Antinode formed slightly below the open (1) 1785 Hz (2) 1968 Hz (3) 1950 Hz (4) 2130 Hz 107. A source of sound of frequency n and a 113. The wavelength of a distant star is 5700 A° listener approach each other with a velocity and the spectral light has a shift of 1.9 A° 1 towards red end then the velocity of star equal to of velocity of sound. The apparent 20 relative to the earth will be: frequency heard by the listener is : (1) 5 × 105 m/sec (2) 2 × 105 m/sec (3) 1.8 × 10 m/sec 5 (4) 1 × 105 m/sec. (1)  21  n (2)  20  n  19   21  114. Two trains A and B are moving in the same direction with velocities 30 m/s and 10 m/s (3)  21  n (4)  19  n respectively. B is behind from A and A blows  20   20  a horn of frequency 450 Hz. Then the 108. A source of sound of frequency 1000 Hz is apparent frequency heard by observer on moving with a uniform velocity 20 m/s. The train B is (speed of sound is 330 m/s): ratio of apparent frequency heard by the (1) 425 Hz (2) 300 Hz observer before and after the source crosses (3) 450 Hz (4) 350 Hz him would be : [v = 340 m/s] 115. If a star emitting light of wavelength 5000 Å (1) 9 :8 (2) 8:9 (3) 1:1 (4) 9:10 is moving towards earth with a velocity of 109. Two sound sources (of same frequency) are 1.5 × 106 m/s then the shift in the wavelength placed at distance of 100 meter. An observer, due to Doppler's effect will be : when moving between both sources, hears (1) 2.5 Å (2) 250 Å 4 beats per second. The distance between (3) 25 Å (4) Zero sound source is now changed to 400 meter 116. Two stationary sources each emitting waves then the beats/second heard by observer will be of wave length . An observer moves from (1) 2 (2) 4 (3) 8 (4) 16 one source to other with velocity u. Then 110. Doppler effect for sound depends upon the number of beats heard by him :- relative motion of source and listener and it 2u u u also depends upon that which one of these is (1) (2) (3) u (4)   2 in motion. Whereas in doppler effect for light 117. A vehicle, with a horn of frequency n is it only depends upon the relative motion of moving with a velocity of 30 m/s in a the source of light and observer. The reason direction perpendicular to the straight line for it is : joining the observer and the vehicle. The (1) Einstein's mass energy relation observer perceives the sound to have a (2) Einstein's theory of relativity frequency n + n1. Then : (Take velocity of (3) Photo electric effect sound in air 330 m/s) : (4) none of above (1) n1 = 10 n (2) n1 = –n 111. A source of sound of frequency 500 Hz is (3) n1 = 0 (4) n1 = 2n moving towards an observer with velocity 118. Doppler effect for light differs from that for 30 m/s. The speed of sound is 330 m/s. The sound in regards that : frequency heard by the observer will be : (1) 550 Hz (2) 458.3 Hz (1) the relative frequency shift is smaller for light than for sound. (3) 530 Hz (4) 545.5 Hz 112. A bus is moving with a velocity of 5 m/s (2) the velocity addition valid for sound is towards a huge wall. The driver sounds a not true for light waves. horn of frequency 165Hz. If the speed of (3) velocity of light is very large as compared sound in air is 335 m/s, No. of beats heard by to sound. a passenger on bus will be– (4) light waves are electromagnetic waves (1) 6 (2) 5 (3) 3 (4) 4 but sound waves are mechanical. 119. If a source is moving away from a stationary 122. An observer moves towards a stationary observer with half of velocity of sound. The source of sound with a speed 1/5th of the frequency observed will be :- speed of sound. The wavelength and (1) one-third (2) doubled frequency of the source are  and f (3) halved (4) two-third respectively. The apparent frequency and 120. A siren emitting sound of frequency 800 Hz is wavelength recorded by the observer are going away, from a static listener, with a speed of 30 m/s. Frequency of sound to be respectively: – heard by the listener is : (Velocity of sound = (1) 1.2f, 1.2 (2) 1.2f,  330 m/s) :- (3) f, 1.2 (4) 0.8f, 0.8 (1) 286.5 Hz (2) 481.2 Hz 123. Velocity of star is 106 m/s and frequency of (3) 733.3 Hz (4) 644.8 Hz emitted light is 4.5 × 1014 Hz. If star is moving 121. As temperature increase, difference between away, then apparent frequency will be : apparent doppler frequency and actual (1) 4.5 Hz. frequency (1) Decreases (2) 4.5 × 1016 Hz. (2) Remains unchanged (3) 4.485 × 1014 Hz. (3) Increases (4) 4.5 × 108 Hz. (4) Depending on frequency, increase or decrease. EXERCISE-I (Conceptual Questions) ANSWER KEY Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Answer 3 3 4 2 2 1 1 4 1 4 1 3 4 1 4 Question 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Answer 3 2 3 1 1 1 4 2 2 4 2 2 3 3 3 Question 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Answer 2 1 2 1 2 2 3 3 3 2 3 3 1 2 4 Question 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Answer 3 1 1 3 3 2 4 3 4 2 2 3 2 1 2 Question 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Answer 3 1 3 4 3 3 2 1 1 3 3 3 4 3 3 Question 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 Answer 4 3 1 4 3 1 2 4 4 1 1 3 2 3 2 Question 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 Answer 1 2 2 3 1 1 3 3 1 3 1 2 2 4 1 Question 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 Answer 4 1 1 2 2 1 2 4 1 3 1 3 2 4 3 Question 121 122 123 Answer 1 2 3 Exercise - II (Previous Year Questions) AIPMT/NEET AIPMT 2006 AIPMT (Pre) 2011 1. Which one of the following statements is 6. Two waves are represented by the true:- equations y1 = asin (t + kx + 0.57) m and (1) Both light and sound waves in air are transverse y2 = a cos (t + kx) m where x is in meter and (2) The sound waves in air are longitudinal t in sec. The phase difference between them is :- while the light waves are transverse (1) 1.0 radian (2) 1.25 radian (3) Both light and sound waves in air are (3) 1.57 radian (4) 0.57 radian longitudinal 7. Sound waves travel at 350 m/s through a (4) Both light and sound waves can travel in warm air and at 3500 m/s through brass. The vacuum AIPMT 2009 wavelength of a 700 Hz acoustic wave as it 2. The driver of a car travelling with speed enters brass from warm air : 30 m/sec towards a hill, sounds a horn of (1) decreases by a factor 10 frequency 600 Hz. If the velocity of sound in air (2) increases by a factor 20 is 330 m/s, the frequency of reflected sound (3) increases by a factor 10 as heard by driver is (1) 500 Hz (2) 550 Hz (4) decreases by a factor 20 (3) 555.5 Hz (4) 720 Hz AIPMT (Mains) 2011 3. A wave in a string has an amplitude of 2cm. 8. Two identical piano wires, kept under the The wave travels in the + ve direction of x axis same tension T have a fundamental frequency with a speed of 128 m/sec and it is noted that of 600 Hz. The fractional increase in the 5 complete waves fit in 4 m length of the tension of one of the wires which will lead to string. The equation describing the wave is :- (1) y = (0.02) m sin (7.85x – 1005t) occurrence of 6 beats/s when both the wires (2) y = (0.02) m sin (7.85x + 1005t) oscillate together would be :- (3) y = (0.02) m sin (15.7x – 2010t) (1) 0.01 (2) 0.02 (4) y = (0.02)m sin (15.7x + 2010t) (3) 0.03 (4) 0.04 AIPMT (Pre) 2010 AIPMT (Pre) 2012 4. A transverse wave is represented by 9. Two sources of sound placed close to each y = A sin (t – kx). For what value of the wavelength is the wave velocity equal to the other, are emitting progressive waves given maximum particle velocity? by y1 = 4 sin 600t and y2 = 5 sin 608t A An observer located near these two sources (1) A (2) 2 will hear :- (3) A (4) 2A (1) 8 beats per second with intensity ratio 5. A tuning fork of frequency 512 Hz makes 81 : 1 between waxing and waning 4 beats per second with the vibrating string of a piano. The beat frequency decreases to (2) 4 beats per second with intensity ratio 2 beats per seconds when the tension in the 81 : 1 between waxing and waning piano string is slightly increased. The (3) 4 beats per second with intensity ratio frequency of the piano string before 25 : 16 between waxing and waning increasing the tension was : (4) 8 beats per second with intensity ratio (1) 508 Hz (2) 510 Hz (3) 514 Hz (4) 516 Hz 25 : 16 between waxing and waning  AIPMT (Mains) 2012 AIPMT 2014 10. The equation of a simple harmonic wave is 14. If n1, n2 and n3 are the fundamental given by : frequencies of three segments into which a  string is divided, then the original y = 3 sin (50 t – x), fundamental frequency n of the string is given 2 where x and y are in metres and t is in by :- seconds. The ratio of maximum particle (1) 1 = 1 + 1 + 1 n n1 n2 n3 velocity to the wave velocity is :- 1 1 1 1 2 (2) = + + (1) 3 (2)  n n1 n2 n3 3 3 (3) n = n1 + n2 + n3 (3) 2 (4)  2 (4) n = n1 + n2 + n3 NEET-UG 2013 15. The number of possible natural oscillations of 11. A wave travelling in the +ve x-direction air column in a pipe closed at one end of having displacement along y-direction as 1m, length 85 cm whose frequencies lie below 1 1250 Hz are: (velocity of sound = 340 ms–1) wavelength 2 m and frequency of Hz is  (1) 4 (2) 5 (3) 7 (4) 6 represented by : AIPMT 2015 (1) y = sin (2x + 2t) 16. The fundamental frequency of a closed organ (2) y = sin (x – 2t) pipe of length 20 cm is equal to the second (3) y = sin (2x – 2t) overtone of an organ pipe open at both the (4) y = sin (10x – 20t) ends. The length of organ pipe open at both 12. A source of unknown frequency gives the ends is :- (1) 100 cm (2) 120 cm 4 beats/s, when sounded with a source of (3) 140 cm (4) 80 cm known frequency 250 Hz. The second RE-AIPMT-2015 harmonic of the source of unknown 17. A source of sound S emitting waves of frequency gives five beats per second, when frequency 100 Hz and an observer O are sounded with a source of frequency 513 Hz. located at some distance from each other. The unknown frequency is The source is moving with a speed of (1) 260 Hz (2) 254 Hz 19.4 ms –1 at an angle of 60° with the source (3) 246 Hz (4) 240 Hz observer line as shown in the figure. The 13. If we study the vibration of a pipe open at observer is at rest. The apparent frequency both ends, then the following statement is not observed by the observer (velocity of sound true : in air 330 ms –1) is :- (1) Pressure change will be maximum at both Vs ends (2) Open end will be antinode (3) Odd harmonics of the fundamental frequency 60° will be generated O (4) All harmonics of the fundamental frequency (1) 97 Hz (2) 100 Hz will be generated (3) 103 Hz (4) 106 Hz 18. A string is stretched between two fixed points 23. Three sound waves of equal amplitudes have separated by 75.0 cm. It is observed to have frequencies (n – 1), n, (n + 1). They superimpose resonant frequencies of 420 Hz and 315 Hz. to give beats. The number of beats produced per There are no other resonant frequencies second will be :- between these two. The lowest resonant (1) 3 (2) 2 (3) 1 (4) 4 NEET(UG) 2017 frequencies for this string is :- 24. The two nearest harmonics of a tube closed at (1) 105 Hz (2) 155 Hz one end and open at other end are 220 Hz and (3) 205 Hz (4) 10.5 Hz 260 Hz. What is the fundamental frequency of NEET-I 2016 the system? 19. A siren emitting a sound of frequency 800 Hz (1) 20 Hz (2) 30 Hz moves away from an observer towards a cliff (3) 40 Hz (4) 10 Hz at a speed of 15ms–1. Then, the frequency of 25. Two cars moving in opposite directions sound that the observer hears in the echo approach each other with speed of 22 m/s reflected from the cliff is : and 16.5 m/s respectively. The driver of the (Take velocity of sound in air = 330 ms–1) first car blows a horn having a frequency 400 (1) 765 Hz (2) 800 Hz Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s] :- (3) 838 Hz (4) 885 Hz (1) 361 Hz (2) 411 Hz 20. A uniform rope of length L and mass m1 hangs (3) 448 Hz (4) 350 Hz vertically from a rigid support. A block of NEET(UG) 2018 mass m2 is attached to the free end of the 26. A tuning fork is used to produce resonance in a rope. glass tube. The length of the air column in this A transverse pulse of wavelength 1 is tube can be adjusted by a variable piston. At produced at the lower end of the rope. The room temperature of 27°C two successive wavelength of the pulse when it reaches the resonances are produced at 20 cm and 73 cm top of the rope is 2. The ratio 2/1 is : column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at m1 m1 + m2 27°C is:- (1) (2) m2 m2 (1) 330 m/s (2) 339 m/s m2 m1 + m2 (3) 350 m/s (4) 300 m/s (3) (4) 27. The fundamental frequency in an open organ m1 m1 pipe is equal to the third harmonic of a closed 21. An air column, closed at one end and open at organ pipe. If the length of the closed organ the other, resonates with a tuning fork when pipe is 20 cm, the length of the open organ the smallest length of the column is 50 cm. pipe is :- The next larger length of the column (1) 13.2 cm (2) 8 cm resonating with the same tuning fork is : (3) 12.5 cm (4) 16 cm (1) 66.7 cm (2) 100 cm NEET(UG) 2019 (Odisha) 28. A tuning fork with frequency 800 Hz (3) 150 cm (4) 200 cm produces resonance in a resonance column NEET-II 2016 tube with upper end open and lower end 22. The second overtone of an open organ pipe closed by water surface. Successive has the same frequency as the first overtone resonance are observed at length 9.75 cm, of a closed pipe L metre long. The length of the 31.25 cm and 52.75 cm. The speed of sound in open pipe will be air is :- L (1) 500 m/s (2) 156 m/s (1) (2) 4 L (3) L (4) 2 L (3) 344 m/s (4) 172 m/s  NEET(UG) 2020 NEET(UG) 2022 29. In a guitar, two strings A and B made of same 31. If the initial tension on a stretched string is material are slightly out of tune and produce doubled, then the ratio of the initial and final beats of frequency 6 Hz. When tension in B is speeds of a transverse wave along the string slightly decreased, the beat frequency increases is: to 7 Hz. If the frequency of A is 530 Hz, the (1) 2 :1 (2) 1: 2 original frequency of B will be: (3)1 : 2 (4) 1 : 1 (1) 537 Hz (2) 523 Hz RE-NEET(UG) 2022 (3) 524 Hz (4) 536 Hz 32. An organ pipe filled with a gas at 27°C NEET(UG) 2020 (Covid-19) resonates at 400 Hz in its fundamental 30. The length of the string of a musical mode. If it is filled with the same gas at 90°C, instrument is 90 cm and has a fundamental the resonance frequency at the same mode frequency of 120 Hz. Where should it be will be :- pressed to produce fundamental frequency of (1) 420 Hz (2) 440 Hz 180 Hz? (3) 484 Hz (4) 512 Hz (1) 75 cm (2) 60 cm (3) 45 cm (4) 80 cm EXERCISE-II (Previous Year Questions) ANSWER KEY Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Answer 2 4 1 4 1 1 3 2 2 4 2 2 1 1 4 Question 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Answer 2 3 1 3 2 3 4 2 1 3 2 1 3 3 2 Question 31 32 Answer 2 2 Exercise - III 1. Given below are two statements: 4. The equation of travelling wave is given by Statement I : For same length but different (all quantities are in SI units) y = 0.02 sin 2 gas COP fundamental frequency are different. (10t – 5x) Statement II : For same length but different Column-I Column-II gas COP fundamental wavelength remains i Speed of wave a 20  same. ii Angular frequency b 0.4  In light of above statement choose the most of wave appropriate answer from the options given iii Wavelength of wave c 2 below: (1) Both statement I and statement II are iv Maximum particle d 0.2 correct. speed (2) Statement I is correct and statement II is (1) i → c, ii → a, iii → d, iv → c incorrect. (2) i → a, ii → b, iii → c, iv → d (3) Statement I is incorrect and statement II is (3) i → c, ii → b, iii → a, iv → d correct. (4) i → c, ii → a, iii → d, iv → b (4) Both statements I and statements II are 5. In a resonance tube experiment, a close organ incorrect. pipe of length 120 cm resonate when tuned with 2. Given below are two statements: a tuning fork of frequency 340 Hz. If water is Statement I : Mechanical transverse waves poured in the pipe then (given vair = 340m/sec.): cannot be generated in gaseous medium. (a) Minimum length of water column to have Statement II : Mechanical transverse waves the resonance is 45 cm. can be produced only in such medium which (b) The distance between two successive have shearing property. nodes is 50 cm. In light of above statement choose the most (c) The maximum length of water column to appropriate answer from the options given create the resonance is 95 cm below: (d) None of these (1) Both statement I and statement II are correct. Choose the correct statements : (2) Statement I is correct and statement II is (1) a, b, c (2) b, c (3) a, c (4) None incorrect. 6. Regarding speed of sound in gas match the (3) Statement I is incorrect and statement II is following - correct. Column-I Column-II (4) Both statements I and statements II are i Temperature of gas a Speed incorrect. is made 4 times and becomes 3. Consider the following statements : pressure 2 times 2 2 times Statement I : The velocity of sound in the air ii Only pressure is b Speed increases due to presence of moisture in it. made 4 times becomes Statement II : The presence of moisture in air without change in two times lowers the density of air. temperature In light of above statement choose the most iii Only temperature c Speed appropriate answer from the options given changed to 4 times remain below: unchanged (1) Both statement I and statement II are iv Molecular mass of d Speed correct. the gas is made 4 become half (2) Statement I is correct and statement II is incorrect. times (3) Statement I is incorrect and statement II is (1) i → a, ii → c, iii → d, iv → b correct. (2) i → b, ii → c, iii → d, iv → a (4) Both statements I and statements II are (3) i → b, ii → c, iii → b, iv → d incorrect. (4) i → c, ii → b, iii → a, iv → c 7. For a closed organ pipe match the following : Reason (R) : In a closed pipe 2 = 31. Column-I Column-II In the light of the above statements, choose i Third overtone a 3 the most appropriate answer from the frequency is x times the options given below: fundamental frequency. (1) Both (A) and (R) are true and (R) is the Here, x is equal to correct explanation of (A). ii No. of nodes in second b 4 overtone (2) Both (A) and (R) are true and (R) is NOT iii No. of antinode in third c 5 the correct explanation of (A). overtone (3) (A) is true but (R) is false. d None (4) (A) is false but (R) is true. (1) i → a, ii → d, iii → b 11. Given below are two statements: One is (2) i → d, ii → a, iii → b labelled as Assertion (A) and the other is (3) i → b, ii → a, iii → d labelled as Reason (R). (4) i → c, ii → d, iii → b Assertion (A) : In stationary waves, energy is 8. In a stationary wave pattern, all the particles - confined within the wave region. (a) of the medium vibrate in the same phase Reason (R) : Every particle is stationary in a (b) in the region between two antinodes stationary wave. vibrate in the same phase In the light of the above statements, choose (c) in the region between two successive the most appropriate answer from the nodes vibrate in the same phase options given below: (d) on either side of a node vibrate in (1) Both (A) and (R) are true and (R) is the opposite phase correct explanation of (A). Choose the correct statement : (2) Both (A) and (R) are true and (R) is NOT (1) a, c, d (2) a, b, c, d the correct explanation of (A). (3) c, d (4) a, b, c (3) (A) is true but (R) is false. 9. Given below are two statements: One is (4) (A) is false but (R) is true. labelled as Assertion (A) and the other is labelled as Reason (R). 12. Given below are two statements: One is Assertion (A) : Sound travels faster on a labelled as Assertion (A) and the other is rainy day than on a dry day. labelled as Reason (R). Reason (R) : Moisture increases the pressure. Assertion (A) : When two vibrating tuning In the light of the above statements, choose forks having frequencies 256 and 512 are the most appropriate answer from the held near each other, beats cannot be heard. options given below: Reason (R) : The principle of superposition (1) Both (A) and (R) are true and (R) is the is valid only if frequencies of oscillators are correct explanation of (A). nearly equal. (2) Both (A) and (R) are true and (R) is NOT In the light of the above statements, choose the correct explanation of (A). the most appropriate answer from the (3) (A) is true but (R) is false. options given below: (4) (A) is false but (R) is true. (1) Both (A) and (R) are true and (R) is the 10. Given below are two statements: One is correct explanation of (A). labelled as Assertion (A) and the other is (2) Both (A) and (R) are true and (R) is NOT labelled as Reason (R). the correct explanation of (A). Assertion (A) : For a closed pipe, the first resonance length is 60 cm. The second (3) (A) is true but (R) is false. resonance position will be obtained at 120 cm. (4) (A) is false but (R) is true. 13. The tension in a stretched string fixed at both 16. Which of the following actions would make a ends in changed by 2%, the fundamental pulse travel faster along a stretched string? frequency is found to get changed by 15 Hz. (A) Move your hand up and down more (a) Wavelength of the string of fundamental frequency does not change quickly as you generate the pulse (b) Velocity of propagation of wave changes (B) Use a heavier string of the same length, by 2% under the same tension (c) Velocity of propagation of wave changes (C) Use a lighter string of the same length, by 1% (d) Original frequency is 1500 Hz under the same tension Choose the correct statement(s) – (D) Stretch the string tighter to increase the (1) a, b, c, d (2) a, b, d tension. (3) a, c, d (4) a, b, c (1) A,B,D (2) B,D (3) C,D (4) A,C 14. Velocity of sound in air is 320 m/s. A pipe closed at one end has a length of 1 m. 17. Sinusoidal waves travel on five identical Neglecting end corrections, the air column in strings. Use the mathematical forms of the the pipe can resonate for sound of frequency. waves given below. In the expressions given (a) 80 Hz (b) 240 Hz below x is in m and y is in millimeters and t is (c) 320 Hz (d) 400 Hz Choose the correct statements: in seconds. (1) a, b, c (2) a, b, d (a) y = (2mm) sin(2x - 4t) (3) b, c, d (4) a, b, c, d (b) y = (3mm) sin(4x - 10t) 15. The equation for the displacement of a (c) y = (2.5mm) sin(6x - 12t) stretched string is given by y = 8 sin2  t x  (d) y = (1mm) sin(8x - 16t)  0.02 − 100  where y and x are in cm and t (e) y = (4mm) sin(10x - 20t)   in second Four of the strings have the same tension, but Column I Column II any one has a different tension. Identify it. (A) Amplitude of wave in (P) 50 (1) a (2) b (3) d (4) e cm 18. A wave disturbance in a medium is described (B) Frequency of wave in (Q) 4 Hz by y (x, t) = 0.02 cos (50 t + /2) cos (10 x), (C) Velocity of wave in ms–1 (R) 4 where x and y are in metres and t in seconds. (D) Maximum particle (S) 5000 (A) A node occurs at x = 0.15 m velocity in cm/s (B) An antinode occurs at x = 0.3 m (T) 400 (C) The speed of the wave is 5.0 m/s Options :- (1) (A) → (Q); (B) → (P); (C) → (P); (D) → (T) (D) The wavelength is 0.2 m (2) (A) → (R); (B) → (S); (C) → (P); (D) → (T) (1) A,C,D (2) B,C,D (3) (A) → (Q); (B) → (P); (C) → (S); (D) → (T) (3) A,B,C,D (4) C,D (4) (A) → (R); (B) → (S); (C) → (S); (D) → (T) EXERCISE-III (Analytical Questions) ANSWER KEY Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Answer 1 1 1 4 1 3 2 3 3 4 3 3 3 2 1 Question 16 17 18 Answer 3 2 3