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Q. No.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)
(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: Â Types of Waves |
Level 3: 35%-60%
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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. \(400 \sqrt 2~\text{m/s}\)
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: Â Wave Motion |
 92%
Level 1: 80%+
JEE
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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:
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: Â Travelling Wave on String |
 72%
Level 2: 60%+
Hints
Consider the following relations regarding propagating waves, where symbols have their usual meanings.
Which of these equation(s) correctly describes a wave?
| (a) | \(\dfrac{\partial y}{\partial t}=\left ( \dfrac{\omega }{k} \right )^{2}\dfrac{\partial y}{\partial x} \) |
| (b) | \(\dfrac{\partial^{2}y}{\partial t^{2}}=\left ( \dfrac{\omega }{k} \right )^{2}\dfrac{\partial^{2}y}{\partial x^{2}}\) |
| 1. | only (a) | 2. | only (b) |
| 3. | both (a) and (b) | 4. | neither (a) nor (b) |
Subtopic: Â Types of Waves |
 69%
Level 2: 60%+
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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: Â Speed of Sound |
 76%
Level 2: 60%+
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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. \(2:3\)
1. \(\sqrt 3:\sqrt 2\)
2. \(3:2\)
3. \(9:4\)
4. \(2:3\)
Subtopic: Â Energy of Waves |
 83%
Level 1: 80%+
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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 \(=330~\text{m/s}\) )
( the velocity of sound \(=330~\text{m/s}\) )
| 1. | first harmonic |
| 2. | second harmonic |
| 3. | third harmonic |
| 4. | fourth harmonic |
Subtopic: Â Standing Waves |
 83%
Level 1: 80%+
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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. \(190~\text{Hz}\)
1. \(210~\text{Hz}\)
2. \(209~\text{Hz}\)
3. \(191~\text{Hz}\)
4. \(190~\text{Hz}\)
Subtopic: Â Beats |
 70%
Level 2: 60%+
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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: Â Types of Waves |
 87%
Level 1: 80%+
Hints
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: Â Wave Motion |
 88%
Level 1: 80%+
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