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Q. No.The first overtone of a closed pipe has a frequency \(f_c.\) A frequency that is \(2f_c\) can be excited from an open pipe of the same length but vibrating in its:
1.
\(2^{\text{nd}}\) harmonic
2.
\(3^{\text{rd}}\) harmonic
3.
\(6^{\text{th}}\) harmonic
4.
\(12^{\text{th}}\) harmonic
Subtopic: Â Standing Waves |
 68%
Level 2: 60%+
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The equation of vibration of a taut string, fixed at both ends, is given by:
\(y=(4~\text{mm})~\cos\Big(\dfrac{\pi x}{30~\text{cm}}\Big)~\sin\Big(400\pi~ \text{s}^{-1}t\Big) .\) The speed of waves on the string is:
1. \(30~\text{m/s}\)
2. \(60~\text{m/s}\)
3. \(90~\text{m/s}\)
4. \(120~\text{m/s}\)
\(y=(4~\text{mm})~\cos\Big(\dfrac{\pi x}{30~\text{cm}}\Big)~\sin\Big(400\pi~ \text{s}^{-1}t\Big) .\) The speed of waves on the string is:
1. \(30~\text{m/s}\)
2. \(60~\text{m/s}\)
3. \(90~\text{m/s}\)
4. \(120~\text{m/s}\)
Subtopic: Â Standing Waves |
 86%
Level 1: 80%+
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A waveform given by: \(y=3A\sin(\omega t-kx)\)
is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
| 1. | \(7A\) | 2. | \(A\) |
| 3. | \(3.5A\) | 4. | \(5A\) |
Subtopic: Â Wave Motion |
 84%
Level 1: 80%+
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If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
| 1. | \(1:2\) | 2. | \(1:1\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(1:\sqrt{2}\) |
Subtopic: Â Travelling Wave on String |
 72%
Level 2: 60%+
NEET - 2022
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A string of length \(l\) is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is \(2\) mm. The amplitude of a particle at a distance \(l/8\) from the fixed end is:
| 1. | \(2\sqrt2~\text{mm}\) | 2. | \(4~\text{mm}\) |
| 3. | \(\sqrt2~\text{mm}\) | 4. | \(2\sqrt3~\text{mm}\) |
Subtopic: Â Standing Waves |
 55%
Level 3: 35%-60%
NEET - 2022
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A sinusoidal waveform is travelling along the \(x \)-axis. The phase difference between two particles separated by \(10~\text{cm}\) is \(\dfrac\pi{2}{}.\) The wavelength of the wave is:
1. \(20~\text{cm}\)
2. \(30~\text{cm}\)
3. \(40~\text{cm}\)
4. \(80~\text{cm}\)
1. \(20~\text{cm}\)
2. \(30~\text{cm}\)
3. \(40~\text{cm}\)
4. \(80~\text{cm}\)
Subtopic: Â Wave Motion |
 87%
Level 1: 80%+
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An organ pipe filled with a gas at \(27^\circ \text{C}\) resonates at \(400~\text{Hz}\) in its fundamental mode. If it is filled with the same gas at \(90^\circ \text{C},\) the resonance frequency at the same mode will be:
| 1. | \(420~\text{Hz}\) | 2. | \(440~\text{Hz}\) |
| 3. | \(484~\text{Hz}\) | 4. | \(512~\text{Hz}\) |
Subtopic: Â Standing Waves |
 70%
Level 2: 60%+
NEET - 2022
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A string fixed at both ends is under tension \(T.\) It has a length \(L,\) and mass \(m.\) The fundamental frequency of the vibration is:
| 1. | \(\dfrac{ 1}{2L} \sqrt {\dfrac{T}{m}}\) | 2. | \(\dfrac{1}{4 L} \sqrt{\dfrac{T}{m}}\) |
| 3. | \(\dfrac{1}{2} \sqrt{\dfrac{TL}{2m}}\) | 4. | \(\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}\) |
Subtopic: Â Travelling Wave on String |
 56%
Level 3: 35%-60%
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The fundamental frequencies of a closed pipe and an open pipe are identical. The first overtone for the closed pipe is \(f_c\) and for the open pipe is \(f_o.\) Their ratio \(\dfrac{f_c}{f_o}\) is:
| 1. | \(1\) | 2. | \(1/2\) |
| 3. | \(2/3\) | 4. | \(3/2\) |
Subtopic: Â Standing Waves |
 70%
Level 2: 60%+
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Sinusoidal sound waves of the same frequency travelling in air along the \(x\)-axis and the \(y\)-axis arrive in phase with each other at the origin. Their amplitudes are equal to \(A\) (each). The amplitude of the vibration at the origin is:
| 1. | \(A\) | 2. | \(\sqrt 2A\) |
| 3. | \(2A\) | 4. | \((2+\sqrt2)A\) |
Subtopic: Â Wave Motion |
Level 4: Below 35%
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