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A wave travels uniformly in all directions from a point source in an isotropic medium. The displacement of the medium at any point at a distance \(r\) from the source can be represented by:
(where \(A\) is a constant representing the strength of the source)
1. \(\dfrac{A}{\sqrt{r}} \sin (k r-\omega t)\)

2. \(\dfrac{A}{{r}} \sin (k r-\omega t)\)

3. \(Ar \sin (k r-\omega t)\)

4. \(\dfrac{A}{{r^2}} \sin (k r-\omega t)\)
Subtopic:  Types of Waves |
 50%
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In the wave equation, \({y}=0.5 \sin \dfrac{2 \pi}{\lambda}(400 {t}-{x}) ~{\text m}, \) the velocity of the wave will be: 
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
Subtopic:  Wave Motion |
 92%
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A rope of uniform mass per unit length \(\mu\) is suspended from the ceiling, hanging under its own weight. If a small transverse pulse is formed at its lower end \(A\), it travels upward with a local speed \(v=\sqrt {\dfrac{\text{tension}}{\text{mass/length}}}\).
                         
The speed of the pulse is:
1. maximum at \(A,\) minimum at \(O\)
2. minimum at \(A,\) maximum at \(O\)
3. uniform
4. minimum at \(A\) and \(O,\) maximum in the middle
Subtopic:  Travelling Wave on String |
 72%
From NCERT
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Consider the following relations regarding propagating waves, where symbols have their usual meanings.
(a) \(\dfrac{\partial y}{\partial t}=\left ( \dfrac{\omega }{k} \right )^{2}\dfrac{\partial y}{\partial x} \)
(b) \(\dfrac{\partial^{2}y}{\partial t^{2}}=\left ( \dfrac{\omega }{k} \right )^{2}\dfrac{\partial^{2}y}{\partial x^{2}}\)
Which of these equation(s) correctly describes a wave?
1. only (a)  2. only (b) 
3. both (a) and (b)  4. neither (a) nor (b)
Subtopic:  Types of Waves |
 69%
From NCERT
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Given below are two statements: 
Assertion (A): Sound travels faster on a hot summer day than on a cold winter day.
Reason (R): The velocity of sound is directly proportional to the square root of its absolute temperature.
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. (A) is False but (R) is True.
Subtopic:  Speed of Sound |
 76%
From NCERT
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A point source of sound is placed in a non-absorbing medium. Two points \(A\) and \(B\) are at a distance of \(2~\text m\) and \(3~\text m\) from the source, respectively. The ratio of the intensity of the wave at \(A\) to that at \(B\) is:
1. \(\sqrt 3:\sqrt 2\)
2. \(3:2\)
3. \(9:4\)
4. \(2:3\)
Subtopic:  Energy of Waves |
 83%
From NCERT
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A \(30~\text{cm}\) long pipe, open at both ends resonates with a frequency \(1.1~\text{kHz}.\) The mode of vibration will be:
( the velocity of sound \(=330~\text{m/s}\) )
1. first harmonic
2. second harmonic
3. third harmonic 
4. fourth harmonic 
Subtopic:  Standing Waves |
 83%
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A tuning fork of frequency \(200~\text{Hz}\) produced \(10\) beats/sec when sounded with a vibrating sonometer wire. If the tension in the wire is slightly increased the number of beats becomes \(9\) beats/sec. What was the original frequency of the vibrating sonometer wire?
1. \(210~\text{Hz}\)
2. \(209~\text{Hz}\)
3. \(191~\text{Hz}\)
4. \(190~\text{Hz}\)
Subtopic:  Beats |
 70%
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Which of the following is a mechanical wave?
1. Radio waves
2. \(X\text-\)rays
3. Light waves
4. Sound waves

Subtopic:  Types of Waves |
 87%
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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 |
 88%
From NCERT
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