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Q. No.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. \(120~\text{m/s}\)
1. \(30~\text{m/s}\)
2. \(60~\text{m/s}\)
3. \(90~\text{m/s}\)
4. \(120~\text{m/s}\)
Subtopic: Â Standing Waves |
 87%
From NCERT
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The separation between a node and the next antinode in a vibrating air column is \(20\) cm. The speed of sound is \(320\) m/s. The frequency of sound is:
1. \(128\) Hz
2. \(256\) Hz
3. \(400\) Hz
4. \(800\) Hz
Subtopic: Â Standing Waves |
 77%
From NCERT
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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%
From NCERT
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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 |
 67%
From NCERT
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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 |
 54%
From NCERT
NEET - 2022
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The length of a wire between the two ends of a sonometer is \(100~\text{cm}.\) What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio \(1:3:5\)?
| 1. | \(\frac{1500}{23} \mathrm{~cm}, \frac{500}{23} \mathrm{~cm} \) |
| 2. | \(\frac{1500}{23} \mathrm{~cm}, \frac{300}{23} \mathrm{~cm} \) |
| 3. | \(\frac{300}{23} \mathrm{~cm}, \frac{1500}{23} \mathrm{~cm} \) |
| 4. | \(\frac{1500}{23} \mathrm{~cm}, \frac{2000}{23} \mathrm{~cm}\) |
Subtopic: Â Standing Waves |
From NCERT
NEET - 2013
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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. \(512~\text{Hz}\)
1. \(420~\text{Hz}\)
2. \(440~\text{Hz}\)
3. \(484~\text{Hz}\)
4. \(512~\text{Hz}\)
Subtopic: Â Standing Waves |
 69%
From NCERT
NEET - 2022
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