STD 11 - Waves and sound PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 139 questions

51. 51. A tuning fork of frequency \(340\,Hz\) resonates in the fundamental mode with an air column of length \(125\,cm\) in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ \(cm\) (Velocity of sound in air is \(340\,ms ^{-1}\) ) 2022 Hard
52. 52. A wire of length \(30\,cm\), stretched between rigid supports, has it's \(n^{\text {th}}\) and \((n+1)^{\text {th}}\) harmonics at \(400\,Hz\) and \(450\; Hz\), respectively. If tension in the string is \(2700\,N\), it's linear mass density is.........\(kg/m\). 2022 Easy
53. 53. An observer is riding on a bicycle and moving towards a hill at \(18\,km\,h ^{-1}\). He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is \(640\,\,Hz\) and velocity of the sound in air is \(320\,m / s\), the beat frequency between the two sounds heard by observer will be \(...Hz\). 2022 Easy
54. 54. An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be \(\dots \;\)% 2022 Medium
55. 55. In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of \(20.0 \,cm\) for a tuning fork of frequency \(400 \,Hz\) is used. The velocity of the sound at room temperature is \(336 \,ms ^{-1}\). The third resonance is observed when the air column has a length of ......... \(cm\) 2022 Medium
56. 56. In the wave equation \(y =0.5 \sin \frac{2 \pi}{\lambda}(400 t - x )\,m\)  the velocity of the wave will be ......... \(m / s\) 2022 Easy
57. 57. The equations of two waves are given by \(y_{1}=5 \sin 2 \pi(x-v t) \,c m\,\) \(y_{2}=3 \sin 2 \pi(x-v t+1.5) \,c m\) These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........\(cm\) 2022 Medium
58. 58. The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is \(20 \,cm\). The length of the open organ pipe is........\(cm\). 2022 Hard
59. 59. The frequency of echo will be \(.......Hz\) if the train blowing a whistle of frequency \(320\,Hz\) is moving with a velocity of \(36\,km / h\) towards a hill from which an echo is heard by the train driver. Velocity of sound in air is \(330\,m / s\). 2022 Hard
60. 60. The speed of a transverse wave passing through a string of length \(50 \;cm\) and mass \(10\,g\) is \(60\,ms ^{-1}\). The area of cross-section of the wire is \(2.0\,mm ^{2}\) and its Young's modulus is \(1.2 \times 10^{11}\,Nm ^{-2}\). The extension of the wire over its natural length due to its tension will be \(x \times 10^{-5}\; m\). The value of \(x\) is \(...\) 2022 Easy
61. 61. The velocity of sound in a gas. in which two wavelengths \(4.08\,m\) and \(4.16\,m\) produce \(40\) beats in \(12\,s\), will be ..............\(ms ^{-1}\) 2022 Easy
62. 62. Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y=\left(10 \cos \pi x \sin \frac{2 \pi t}{T}\right)\, cm\) The amplitude of the particle at \(x =\frac{4}{3} \,cm\) will be........ \(cm\). 2022 Easy
63. 63. When a car is approaching the observer, the frequency of horn is \(100 Hz\). After passing the observer, it is \(50\,Hz\). If the observer moves with the car, the frequency will be \(\frac{ x }{3} Hz\) where \(x =.....\) 2022 Hard
64. 64. A closed organ pipe of length \(L\) and an open organ pipe contain gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is \(\frac{ x }{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}\) where \(x\) is ......... . (Round off to the Nearest Integer) 2021 Easy
65. 65. A signal of \(0.1\, kW\) is transmitted in a cable. The attenuation of cable is \(-5 \,dB\) per \(km\) and cable length is \(20\, km\). The power received at receiver is \(10^{-x} \, W\). The value of \(x\) is ....... . \(\left[\right.\) Gain in \(\left. dB =10 \log _{10}\left(\frac{ P _{0}}{ P _{i}}\right)\right]\) 2021 Hard
66. 66. A sound wave of frequency \(245 \,Hz\) travels with the speed of \(300\, ms ^{-1}\) along the positive \(x\)-axis. Each point of the wave moves to and fro through a total distance of \(6 \,cm\). What will be the mathematical expression of this travelling wave ? 2021 Medium
67. 67. A source and a detector move away from each other in absence of wind with a speed of \(20\, {m} / {s}\) with respect to the ground. If the detector detects a frequency of \(1800\, {Hz}\) of the sound coming from the source, then the original frequency of source considering speed of sound in air \(340\, {m} / {s}\) will be \({Hz}\) 2021 Easy
68. 68. A student is performing the experiment of resonance column. The diameter of the column tube is \(6 \,cm\). The frequency of the tuning fork is \(504\, Hz\). Speed of the sound at the given temperature is \(336\, m / s\). The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is..........\(cm\) 2021 Hard
69. 69. A tuning fork \(A\) of unknown frequency produces \(5\, beats/s\) with a fork of known frequency \(340\, Hz\). When fork \(A\) is filed, the beat frequency decreases to \(2\, beats/s.\) What is the frequency of fork \(A\) ? (in \(Hz\)) 2021 Hard
70. 70. A tuning fork is vibrating at \(250\, {Hz}\). The length of the shortest closed organ pipe that will resonate with the tuning fork will be ..... \({cm}\) (Take speed of sound in air as \(340\, {ms}^{-1}\) ) 2021 Medium
71. 71. A wire having a linear mass density \(9.0 \times 10^{-4} \;{kg} / {m}\) is stretched between two rigid supports with a tension of \(900\; {N}\). The wire resonates at a frequency of \(500\;{Hz}\). The next higher frequency at which the same wire resonates is \(550\; {Hz}\). The length of the wire is \(...... {m}\) 2021 Hard
72. 72. The amplitude of wave disturbance propagating in the positive \(x\)-direction is given by \(y=\frac{1}{(1+x)^{2}}\) at time \(t=0\) and \(y=\frac{1}{1+(x-2)^{2}}\) at \(t=1\) s, where \(x\) and \(y\) are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be \(...\,{m} / {s}.\) 2021 Medium
73. 73. The frequency of a car horn encountered a change from \(400\, {Hz}\) to \(500\, {Hz}\), when the car approaches a vertical wall. If the speed of sound is \(330\, {m} / {s}\). Then the speed of car is \(.....\,{km} / {h} .\) 2021 Easy
74. 74. The mass per unit length of a uniform wire is \(0.135\, g / cm\). A transverse wave of the form \(y =-0.21 \sin ( x +30 t )\) is produced in it, where \(x\) is in meter and \(t\) is in second. Then, the expected value of tension in the wire is \(x \times 10^{-2} N\). Value of \(x\) is . (Round-off to the nearest integer) 2021 Easy
75. 75. The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by \(4\, \%\), will be ......... \(\%\) 2021 Medium
76. 76. Two cars are approaching each other at an equal speed of \(7.2\, km / hr\). When they see each other, both blow horns having frequency of \(676\, Hz\). The beat frequency heard by each driver will be \(.....\, Hz\). [Velocity of sound in air is \(340\,m / s .]\) 2021 Easy
77. 77. Two cars \({X}\) and \({Y}\) are approaching each other with velocities \(36\; {km} / {h}\) and \(72\; {km} / {h}\) respectively. The frequency of a whistle sound as emitted by a passenger in car \({X}\), heard by the passenger in car \({Y}\) is \(1320 \;{Hz}\). If the velocity of sound in air is \(340\; {m} / {s}\), the actual frequency of the whistle sound produced is ........ \(Hz.\) 2021 Easy
78. 78. Two travelling waves produces a standing wave represented by equation, \({y}=1.0\, {mm} \cos \left(1.57 \,{cm}^{-1}\right) {x} \sin \left(78.5\, {s}^{-1}\right) {t}\) The node closest to the origin in the region \({x}>0\) will be at \({x}=\ldots \ldots \ldots\, {cm}\) 2021 Medium
79. 79. Two waves are simultaneously passing through a string and their equations are : \({y}_{1}={A}_{1} \sin {k}({x}-v {t}), {y}_{2}={A}_{2} \sin {k}\left({x}-{vt}+{x}_{0}\right) .\) Given amplitudes \({A}_{1}=12\, {mm}\) and \({A}_{2}=5\, {mm}\) \({x}_{0}=3.5\, {cm}\) and wave number \({k}=6.28\, {cm}^{-1}\). The amplitude of resulting wave will be \(......\,{mm}\) 2021 Hard
80. 80. Which of the following equations represents a travelling wave ? 2021 Easy
81. 81. A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from \(440\, Hz\) to \(480 \,Hz ,\) when it gets reflected from the wall. If the speed of sound in air is \(345 \,m / s ,\) then the speed of the car is \(.......km/hr\) 2020 Medium
82. 82. A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at \(STP\). Assuming the speed of sound in air at \(STP\) is \(300\; \mathrm{m} / \mathrm{s}\), the frequency difference between the fundamental and second harmonic of this pipe is ___ \(\mathrm{Hz}\) 2020 Hard
83. 83. A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears \(2\; beats/sec\). The oscillation frequency of each tuning fork is \(v_{0}=1400 \;\mathrm{Hz}\) and the velocity of sound in air is \(350\; \mathrm{m} / \mathrm{s}\). The speed of each tuning fork is close to  2020 Hard
84. 84. A transverse wave travels on a taut steel wire with a velocity of \({v}\) when tension in it is \(2.06 \times 10^{4} \;\mathrm{N} .\) When the tension is changed to \(T\). the velocity changed to \(\frac v2\). The value of \(\mathrm{T}\) is close to 2020 Medium
85. 85. A uniform thin rope of length \(12\, m\) and mass \(6\, kg\) hangs vertically from a rigid support and a block of mass \(2\, kg\) is attached to its free end. A transverse short wavetrain of wavelength \(6\, cm\) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \(cm\) ) when it reaches the top of the rope \(?\) 2020 Medium
86. 86. A wire of density \(9 \times 10^{-3} \,kg\, cm ^{-3}\) is stretched between two clamps \(1\, m\) apart. The resulting strain in the wire is \(4.9 \times 10^{-4}\). The lowest frequency of the transverse vibrations in the wire is......\(HZ\) (Young's modulus of wire \(Y =9 \times 10^{10}\, Nm ^{-2}\) ), (to the nearest integer), 2020 Hard
87. 87. A wire of length \(L\) and mass per unit length \(6.0\times 10^{-3}\; \mathrm{kgm}^{-1}\) is put under tension of \(540\; \mathrm{N}\). Two consecutive frequencies that it resonates at are : \(420\; \mathrm{Hz}\) and \(490 \;\mathrm{Hz}\). Then \(\mathrm{L}\) in meters is 2020 Easy
88. 88. Assume that the displacement\((s)\) of air is proportional to the pressure difference \((\Delta p)\) created by a sound wave. Displacement\((s)\) further depends on the speed of sound \((v),\) density of air \((\rho)\) and the frequency \((f)\) If \(\Delta p \approx 10\, Pa , v  \approx 300\, m / s , p  \approx 1\, kg / m ^{3}\) and \(f \approx  1000 \,Hz\), then \(s\) will be the order of (take multiplicative constant to be \(1\) ) 2020 Easy
89. 89. For a transverse wave travelling along a straight line, the distance between two peaks (crests) is \(5 \,m ,\) while the distance between one crest and one trough is \(1.5 \,m\) The possible wavelengths (in \(m\) ) of the waves are 2020 Easy
90. 90. In a resonance tube experiment when the tube is filled with water up to height of \(17.0\, cm\) from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of \(24.5\, cm\). If the velocity of sound in air is \(330\, m / s ,\) the tuning fork frequency is\(......Hz\) 2020 Hard
91. 91. Speed of a transverse wave on a straight wire (mass \(6.0\; \mathrm{g}\), length \(60\; \mathrm{cm}\) and area of cross-section \(1.0\; \mathrm{mm}^{2}\) ) is \(90\; \mathrm{ms}^{-1} .\) If the Young's modulus of wire is \(16 \times 10^{11}\; \mathrm{Nm}^{-2},\) the extension of wire over its natural length is 2020 Easy
92. 92. The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from \(420\, Hz\) to \(490\, Hz ,\) when he hears it after it gets reflected from the wall. Find the speed of the bus (in \(kmh^{-1}\)) if speed of the sound is \(330\, ms ^{-1}\). 2020 Hard
93. 93. Three harmonic waves having equal frequency \(\mathrm{v}\) and same intensity \(\mathrm{I}_{0}\), have phase angles \(0 , \frac{\pi}{4}\) and \(-\frac{\pi}{4}\) respectively. When they are superimposed the intensity of the resultant wave is close to 2020 Medium
94. 94. Two identical strings \(X\) and \(Z\) made of same material have tension \(T _{ x }\) and \(T _{ z }\) in them. If their fundamental frequencies are \(450\, Hz\) and \(300\, Hz ,\) respectively, then the ratio \(T _{ x } / T _{ z }\) is\(.....\) 2020 Easy
95. 95. A closed organ pipe has a fundamental frequency of \(1.5\, kHz\). The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is \(20,000\, Hz\)) 2019 Easy
96. 96. A heavy ball of mass \(M\) is suspended from the ceiling of car by a light string of mass \(m (m << M)\). When the car is at rest, the speed of transverse waves in the string is \(60\, ms^{-1}\). When the car has acceleration \(a\) , the wave-speed increases to \(60.5\, ms^{-1}\). The value of \(a\) , in terms of gravitational acceleration \(g\) is closest to 2019 Hard
97. 97. 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...... \(Hz\) 2019 Easy
98. 98. A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \(60^o\) with ground level. But he finds the aeroplane right vertically above his position. If \(\upsilon \) is the speed of sound, speed of the plane is 2019 Easy
99. 99. A progressive wave travelling along the positive \(x-\) direction is represented by \(y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)\). Its snapshot at \(t = 0\) is given in the figure For this wave, the phase \(\phi \) is
    2019 Medium
100. 100. A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency \(512\,Hz\) produces first resonance when the tube is filled with water to a mark \(11\,cm\) below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency \(256\,Hz\) which produces first resonance when water reaches a mark \(27\,cm\) below the reference mark. The velocity of sound in air, obtained in the experiment, is close to .... \(ms^{-1}\) 2019 Medium

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