Wave Motion & Waves on String PYQs Set 3 (PDF)

Set 3 of 5 · Questions 61-90 of 141

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Motion & Waves on String · Set 3 (Q61-90)
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61. $The equation of a simple harmonic wave is given by y = 3 sin \frac{π}{2} (50 t - x) Where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is$ (1) $2$ (2) $\frac{3}{2} π$ (3) $3π$ (4) $\frac{2}{3} π$ 62. $A wave of frequency 100 Hz travels along a string towards its fixed end. When this wave travels back, after reflection, a node is formed at a distance of 10 cm from the fixed end. The speed of the wave (incident and reflected) is$ (1) $20 m / s$ (2) $40 m / s$ (3) $5 m / s$ (4) $10 m / s .$ 63. $Find the wrong statement from the following about the equation of stationary wave given by Y = 0.04 cos (πx) sin (50 πt) m where t is in second. Then for the stationary wave$ (1) $Time period = 0.02 s$ (2) $Wavelength = 2 m$ (3) $Velocity = 50 m / s$ (4) $Amplitude = 0.02 m$ 64. $Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 m m^{2}) is 90 m s^{-1} . If the Young's modules of wire is 16 \times 1 0^{11} N m^{-2}, the extension of wire over its natural length is:$ (1) $0.02 mm$ (2) $0.01 mm$ (3) $0.03 mm$ (4) $0.04 mm$ 65. $Which one of the following statements is true?$ (1) $both light and sound waves can travel in vacuum$ (2) $both light and sound waves in air are transverse$ (3) $the sound waves in air are longitudinal while the light waves are transverse$ (4) $both light and sound waves in air are longitudinal.$ 66. $Sound waves travel at 350 m / s through a warm air and at 3500 m / s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air$ (1) $decrease by a factor 10$ (2) $increase by a factor 20$ (3) $increase by a factor 10$ (4) $decrease by a factor 20$ 67. $Three harmonic waves having equal frequency v and same intensity I_{0}, have phase angles 0, \frac{π}{4} and - \frac{π}{4} respectively. When they are superimposed the intensity of the resultant wave is close to:$ (1) $5.8 I_{0}$ (2) $3 I_{0}$ (3) $I_{0}$ (4) $0.2 I_{0}$ 68. $A progressive wave is represented by y = 12 sin (5 t - 4 x) cm . On this wave, how far away are the two points having phase difference of 90^{\circ} ?$ (1) $\frac{π}{2} cm$ (2) $\frac{π}{4} cm$ (3) $\frac{π}{8} cm$ (4) $\frac{π}{16} cm$ 69. $The 0equations of two waves are given by: y_{1} = 5 sin 2 π (x - vt) cm y_{2} = 3 sin 2 π (x - vt + 1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is$ (1) $2 cm$ (2) $4 cm$ (3) $5.8 cm$ (4) $8 cm$ 70. $A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is: (take g = 10 m s^{-2})$ (1) $2 s$ (2) $22 s$ (3) $2 s$ (4) $2 π 2 s$ 71. $A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 \times 10^{4} N . When the tension is changed to T, the velocity changed to v /2 . The value of T is close to:$ (1) $5.15 \times 10^{3} N$ (2) $10.2 \times 10^{2} N$ (3) $2.50 \times 10^{4} N$ (4) $30.5 \times 10^{4} Ns$ 72. $A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:$ (1) $333 Hz$ (2) $753 Hz$ (3) $666 Hz$ (4) $500 Hz$ 73. $A sonometer wire 49 cm long is in unison with a tuning fork of frequency ' n'. If the length of the wire is decreased by 1 cm and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of ' n' is$ (1) $256 Hz$ (2) $320 Hz$ (3) $288 Hz$ (4) $384 Hz$ 74. $Displacement of a wave is expressed as x (t) = 5 co s (628 t + \frac{π}{2}) m . The wavelength of the wave when its velocity is \frac{300 m}{s} is: (π = 3.14)$ (1) $0.33 m$ (2) $0.5 m$ (3) $3 m$ (4) $5 m$ 75. $A wire under tension vibrates with a fundamental frequency of 600 Hz . If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one-ninth the tension. Then the fundamental frequency will become$ (1) $200 Hz$ (2) $300 Hz$ (3) $600 Hz$ (4) $400 Hz$ 76. $Which one of the following represents a wave?$ (1) $y = A sin (ωt - kx)$ (2) $y = A cos (at - bx + c)$ (3) $y = A sin kx$ (4) $y = A sin ωt .$ 77. $' n' number of waves are produced on a string in 0.5 second. Now the tension in the string is doubled (Assume length and radius constant), the number of waves produced in 0.5 second for the same harmonic will be$ (1) $n$ (2) $2 n$ (3) $\frac{n}{2}$ (4) $\frac{n}{5}$ 78. $A string vibrates with a frequency of 200 Hz . When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz . The ratio of the new tension to the original tension is$ (1) $3 : 1$ (2) $1 : 3$ (3) $9 : 1$ (4) $1 : 9$ 79. $The length of the string of a musical instrument is 90 cm and has a fundamental frequency of 120 Hz. Where should it be pressed to produce fundamental frequency of 180 Hz? [NEET 2020]$ (1) $75 cm$ (2) $60 cm$ (3) $45 cm$ (4) $80 cm$ 80. $A uniform rope of length L and mass m_{1} hangs vertically from a rigid support. A block of mass m_{2} is attached to the free ends of the rope. A transverse pulse of wavelength λ_{1} is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is λ_{2} . The ratio λ_{2} / λ_{1} is [NEET 2016]$ (1) $\frac{m _{1} + m _{2}}{m _{2}}$ (2) $\frac{m _{2}}{m _{1}}$ (3) $\frac{m _{1} + m _{2}}{m _{1}}$ (4) $\frac{m _{1}}{m _{2}}$ 81. $A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 \times 1 0^{3} kg/ m^{3} and its Young's modulus is 9.27 \times 1 0^{10} Pa. What will be the fundamental frequency of the longitudinal vibrations?$ (1) $10kHz$ (2) $7.5kHz$ (3) $5kHz$ (4) $2.5kHz$ 82. $The length and diameter of a metal wire is doubled. The fundamental frequency of vibration will change from ' n' to (Tension being kept constant and material of both the wires is same)$ (1) $\frac{n}{4}$ (2) $\frac{n}{8}$ (3) $\frac{n}{12}$ (4) $\frac{n}{16}$ 83. $A stationary wave is represented by y = A sin (100 t) cos (0.01 x), where y and A are in millimetres, t is in seconds and x is in metres. The velocity of the wave is$ (1) $1 0^{4} m / s$ (2) $not derivable$ (3) $1 m / s$ (4) $1 0^{2} m / s .$ 84. $Two waves having equation x_{1} = a sin (ωt - kx + φ_{1}), x_{2} = a sin (ωt - kx + φ_{2}) If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is$ (1) $\frac{π}{6}$ (2) $\frac{2 π}{3}$ (3) $\frac{π}{4}$ (4) $\frac{π}{3} .$ 85. $A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 A^{0} between them. The wavelength of the standing wave is$ (1) $6.05 A^{0}$ (2) $2.42 A^{0}$ (3) $1.21 A^{0}$ (4) $3.63 A^{0}$ 86. $A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 \times 10^{4} N . When the tension is changed to T, the velocity changed to v /2 . The value of T is close to:$ (1) $5.15 \times 10^{3} N$ (2) $8.24 \times 10^{4} N$ (3) $6 \times 10^{4}$ (4) $5.15 \times 10^{4} N$ 87. $Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is_____degree.$ 88. $In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is______g.$ 89. $A transverse harmonic wave on a string is given by y(x, t)= 5 sin(6t + 0. 003x) where x and y are in cm and t in sec. The wave velocity is_________m s^{- 1}$ 90. $Two waves are simultaneously passing through a string and their equations are: y_{1} = A_{1} sin k (x - vt), y_{2} = A_{2} sin k (x - vt + x_{0}) . Given amplitudes A_{1} = 12 mm and A_{2} = 5 mm x_{0} = 3.5 cm and wave number k = 6.28 c m^{- 1} . The amplitude of resulting wave will be mm$