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Q. No.The equation of a plane progressive wave is given by \(y=5 \cos \pi\left(200 t-\dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is: (in m/s)
1. \(120\)
2. \(150\)
3. \(200\)
4. \(300\)
1. \(120\)
2. \(150\)
3. \(200\)
4. \(300\)
Subtopic: Travelling Wave on String |
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A transverse wave on a string is described by \(y=3 \sin (36 t+0.018 x+\pi / 4) .\) where \( x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is: (in cm) (Nearest integer)
1. \(300\)
2. \(200\)
3. \(349\)
4. \(450\)
1. \(300\)
2. \(200\)
3. \(349\)
4. \(450\)
Subtopic: Wave Motion |
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Level 2: 60%+
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Two strings \((A,B)\) having linear densities \(\mu_A = 2\times 10^{-4}~\text{kg/m}\) and \(\mu_B = 4\times 10^{-4}~\text{kg/m}\) and lengths \(L_A =2.5~\text{m}\) and \(L_B = 1.5~\text{m}\) respectively are joined. Free ends of \(A\) and \(B\) are tied to two rigid supports \(C\) and \(D\), respectively creating a tension of \(500~\text{N}\) in the wire. Two identical pulses, sent from \(C\) and \(D\) ends, take time \(t_1\) and \(t_2\), respectively, to reach the joint. The ratio \(\dfrac{t_1}{t_2}\) is:
1. \(1.08\)
2. \(1.90\)
3. \(1.67\)
4. \(1.18\)
1. \(1.08\)
2. \(1.90\)
3. \(1.67\)
4. \(1.18\)
Subtopic: Speed of Sound |
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In an open organ pipe \(v_3\) and \(v_6\) are \(3^{\text{rd}}\) and \(6^{\text{th}}\) harmonic frequencies, respectively. If \(v_6 -v_3 =2200~\text{Hz}\) then length of the pipe is: (in mm)
1. \(275\)
2. \(225\)
3. \(200\)
4. \(250\)
1. \(275\)
2. \(225\)
3. \(200\)
4. \(250\)
Subtopic: Standing Waves |
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The velocity of sound in air is doubled when the temperature is raised from \(0^{\circ}\text{C}\) to \(\alpha^{\circ}\text{C}\). The value of \(\alpha\) is:
1. \(700\)
2. \(819\)
3. \(500\)
4. \(600\)
1. \(700\)
2. \(819\)
3. \(500\)
4. \(600\)
Subtopic: Speed of Sound |
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The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \(\dfrac{5}{x}\). The value of \(x\) is:
1. \(4\)
2. \(2\)
3. \(1\)
4. \(3\)
1. \(4\)
2. \(2\)
3. \(1\)
4. \(3\)
Subtopic: Standing Waves |
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The speed of a longitudinal wave in a metallic bar is \(400~\text{m/s}\). If the density and Young's modulus of the bar material are increased by \(0.5\%\) and \(1\%\) respectively then the speed of the wave is changed approximately to: (in m/s)
1. \(399\)
2. \(398\)
3. \(402\)
4. \(401\)
1. \(399\)
2. \(398\)
3. \(402\)
4. \(401\)
Subtopic: Speed of Sound |
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Two tuning forks \(A\) and \(B\) are sounded together giving rise to \(8\) beats in \(2~\text{s}\). When fork \(A\) is loaded with wax, the beat frequency is reduced to \(4\) beats in \(2~\text{s}\). If the original frequency of tuning fork \(B\) is \(380~\text{Hz}\), then the original frequency of tuning fork \(A\) is: (in Hz)
1. \(384\)
2. \(376\)
3. \(380\)
4. \(390\)
1. \(384\)
2. \(376\)
3. \(380\)
4. \(390\)
Subtopic: Beats |
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Displacement of a wave is expressed as \(x(t) = 5\cos(628t+\pi/2)~\text m. \) The wavelength of the wave when its velocity is \(300 ~\text{m/s} \) is: \((\pi=3.14 )\)
1. \(5~\text m\)
2. \(0.5~\text m\)
3. \(3~\text m\)
4. \(0.33~\text m\)
1. \(5~\text m\)
2. \(0.5~\text m\)
3. \(3~\text m\)
4. \(0.33~\text m\)
Subtopic: Wave Motion |
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In an experiment with a closed organ pipe, it is filled with water by one fifth of its volume. The frequency of the fundamental note will change by:
1. \(25\%\)
2. \(20\%\)
3. \(-20\% \)
4. \(-25\%\)
1. \(25\%\)
2. \(20\%\)
3. \(-20\% \)
4. \(-25\%\)
Subtopic: Standing Waves |
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Level 1: 80%+
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