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Q. No.A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio:
1.
\(1:2\)
2.
\(2:3\)
3.
\(3:4\)
4.
\(4:5\)
Subtopic: Standing Waves |
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Three waves of equal frequency having amplitudes of \(10~\mu \text{m}, 4~\mu \text{m}~\text{and}~7~\mu\text{m}\) arrive at a given point with a successive phase difference of \(\frac{\pi}{2}.\) The amplitude of the resulting wave \((\text{in}~\mu \text{m})\) is given by:
1. \(7\)
2. \(6\)
3. \(5\)
4. \(4\)
1. \(7\)
2. \(6\)
3. \(5\)
4. \(4\)
Subtopic: Standing Waves |
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An organ pipe that is closed at one end has a fundamental frequency of \(1500~\text{Hz}\). The maximum number of overtones generated by this pipe that a normal person can hear is:
| 1. | \(14\) | 2. | \(13\) |
| 3. | \(6\) | 4. | \(9\) |
Subtopic: Standing Waves |
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Level 2: 60%+
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The equation of a stationary wave is \(y = 0.8\cos\left(\frac{\pi x}{20}\right)\sin200(\pi t)\), where \(x\) is in \(\text{cm}\) and \(t\) is in \(\text{sec}.\) The separation between consecutive nodes will be:
1. \(20~\text{cm}\)
2. \(10~\text{cm}\)
3. \(40~\text{cm}\)
4. \(30~\text{cm}\)
1. \(20~\text{cm}\)
2. \(10~\text{cm}\)
3. \(40~\text{cm}\)
4. \(30~\text{cm}\)
Subtopic: Standing Waves |
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Two tuning forks, \(A\) and \(B\), vibrating simultaneously produce \(5\) beats. The frequency of \(B\) is \(512~\text{Hz}\). It is seen that if one arm of \(A\) is filed a little, then the number of beats increases. The frequency of \(A\) in Hz will be:
| 1. | \(502\) | 2. | \(507\) |
| 3. | \(517\) | 4. | \(522\) |
Subtopic: Beats |
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Tuning fork \(F_1\) has a frequency of \(256~\text{Hz}\) and it is observed to produce \(6\) beats/second with another tuning fork \(F_2\). When \(F_2\) is loaded with wax, it still produces \(6\) beats/second with \(F_1\). The frequency of \(F_2\) before loading was:
1. \(253~\text{Hz}\)
2. \(262~\text{Hz}\)
3. \(250~\text{Hz}\)
4. \(259~\text{Hz}\)
1. \(253~\text{Hz}\)
2. \(262~\text{Hz}\)
3. \(250~\text{Hz}\)
4. \(259~\text{Hz}\)
Subtopic: Beats |
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Two waves are propagating to the point \(P\) along a straight line produced by two sources, \(A\) and \(B\), of simple harmonic and equal frequency. The amplitude of every wave at \(P\) is \(a\) and the phase of \(A\) is ahead by \(\frac{\pi}{3}\) than that of \(B\), and the distance \(AP\) is greater than \(BP\) by \(50~\text{cm}\). If the wavelength is \(1~\text{m}\), then the resultant amplitude at point \(P\) will be:
1. \(2a\)
2. \(a\sqrt{3}\)
3. \(a\sqrt{2}\)
4. \(a\)
1. \(2a\)
2. \(a\sqrt{3}\)
3. \(a\sqrt{2}\)
4. \(a\)
Subtopic: Standing Waves |
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The equation of a progressive wave is given by \(y = 4\sin\left\{ \pi\left(\frac{t}{5}-\frac{x}{9}\right)+\frac{\pi}{6}\right\}\), where \(x\) and \(y\) are in metres and \(t\) in seconds.
Which of the following is correct?
1. \(v = 5~\text{m/s}\)
2. \(\lambda = 18~\text{m}\)
3. \(A = 0.04~\text{m}\)
4. \(\nu= 50~\text{Hz}\)
Which of the following is correct?
1. \(v = 5~\text{m/s}\)
2. \(\lambda = 18~\text{m}\)
3. \(A = 0.04~\text{m}\)
4. \(\nu= 50~\text{Hz}\)
Subtopic: Wave Motion |
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Level 1: 80%+
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The wave equations of two particles are given by \(y_1=a\sin(\omega t-kx), y_2 = a \sin(kx+\omega t),\) then:
| 1. | they are moving in the opposite direction. |
| 2. | the phase between them is \(90^{\circ}\). |
| 3. | the phase between them is \(45^{\circ}\). |
| 4. | the phase between them is \(0^{\circ}\). |
Subtopic: Wave Motion |
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The displacement of a particle is given by \(y = 5\times 10^{-4}\sin\left(100t-50x\right),\) where \(x\) is in metres and \(t\) is in seconds. The velocity of the wave is:
1. \(5000~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.5~\text{m/s}\)
4. \(300~\text{m/s}\)
1. \(5000~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.5~\text{m/s}\)
4. \(300~\text{m/s}\)
Subtopic: Wave Motion |
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Level 1: 80%+
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