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Q. No.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:
1. \(282.8\) ms–1
2. \(175.5\) ms–1
3. \(353.6\) ms–1
4. \(707.2\) ms–1
Subtopic: Beats |
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A tunning fork of frequency \(340~\text{Hz}\) resonates in the fundamental mode with an air column of length \(125~\text{cm}\) 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: (Velocity of sound in air is \(340\) ms-1)
1. \(75~\text{cm}\)
2. \(50~\text{cm}\)
3. \(25~\text{cm}\)
4. \(45~\text{cm}\)
1. \(75~\text{cm}\)
2. \(50~\text{cm}\)
3. \(25~\text{cm}\)
4. \(45~\text{cm}\)
Subtopic: Standing Waves |
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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:
1. \(20\text{%}\)
2. \(10\text{%}\)
3. \(5\text{%}\)
4. \(0\text{%}\)
1. \(20\text{%}\)
2. \(10\text{%}\)
3. \(5\text{%}\)
4. \(0\text{%}\)
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A set of \(20\) tuning forks is arranged in a series of increasing frequencies. If each fork gives \(4\) beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of the last fork is:
1. \(152~\text{Hz}\)
2. \(234~\text{Hz}\)
3. \(134~\text{Hz}\)
4. \(144~\text{Hz}\)
1. \(152~\text{Hz}\)
2. \(234~\text{Hz}\)
3. \(134~\text{Hz}\)
4. \(144~\text{Hz}\)
Subtopic: Beats |
77%
From NCERT
JEE
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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 \(y =10 \cos ( π x ) \sin \left( \frac{2 π t} {T}\right ) ~\text{cm}.\) The amplitude of the particle at \(x =\frac{4}{3}~\text{cm}\) will be:
1. \(5 ~\text{cm}\)
2. \(10 ~\text{cm}\)
3. \(15 ~\text{cm}\)
4. \(20 ~\text{cm}\)
1. \(5 ~\text{cm}\)
2. \(10 ~\text{cm}\)
3. \(15 ~\text{cm}\)
4. \(20 ~\text{cm}\)
Subtopic: Standing Waves |
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The equations of two waves are given by:
\(\begin{aligned} &\mathrm{y}_1=5 \sin 2 \pi(x-v t) \mathrm{cm} \\ &\mathrm{y}_2=3 \sin 2 \pi(\mathrm{x}-\mathrm{vt}+1.5) \mathrm{cm} \end{aligned}\)
These waves are simultaneously passing through a string. The amplitude of the resulting wave is:
1. 2 cm
2. 4 cm
3. 5.8 cm
4. 8 cm
\(\begin{aligned} &\mathrm{y}_1=5 \sin 2 \pi(x-v t) \mathrm{cm} \\ &\mathrm{y}_2=3 \sin 2 \pi(\mathrm{x}-\mathrm{vt}+1.5) \mathrm{cm} \end{aligned}\)
These waves are simultaneously passing through a string. The amplitude of the resulting wave is:
1. 2 cm
2. 4 cm
3. 5.8 cm
4. 8 cm
Subtopic: Standing Waves |
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A transverse wave travels along a uniform wire with a length of \(50\) cm and a mass of \(10~\text{grams}\) at a speed of \(60\) m/s. If the wire has a cross-sectional area of \(2.0\) mm2 and a Young's modulus of \(1.2\times 10^{11}\) N/m2, the extension of the wire over its natural length due to its tension will be:
| 1. | \(0.12\) mm | 2. | \(0.15\) mm |
| 3. | \(0.20\) mm | 4. | \(0.25\) mm |
Subtopic: Travelling Wave on String |
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In an experiment to determine the velocity of sound in air at room temperature, 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:
1. \(100\) cm
2. \(110\) cm
3. \(104\) cm
4. \(120\) cm
1. \(100\) cm
2. \(110\) cm
3. \(104\) cm
4. \(120\) cm
Subtopic: Standing Waves |
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A longitudinal wave is represented by \(x = 10 ~\sin ~2 \pi \left( nt- {\dfrac x \lambda}\right)\) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:
| 1. | \(2 \pi\) cm | 2. | \(5 \pi\) cm |
| 3. | \(\pi\) cm | 4. | \({\dfrac {5 \pi} 2}\) cm |
Subtopic: Wave Motion |
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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. The frequency of echo will be:
(The velocity of sound in air is \(330\) m/s.)
1. \(430\) Hz
2. \(340\) Hz
3. \(120\) Hz
4. \(220\) Hz
(The velocity of sound in air is \(330\) m/s.)
1. \(430\) Hz
2. \(340\) Hz
3. \(120\) Hz
4. \(220\) Hz
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