Q. No.A wave traveling along a string is described by;
\(y(x,t)=0.004 \text{sin}(80x-4t)\)
in which the numerical constants are in SI units. The amplitude and the time period of the wave are, respectively:
1. \(0.004~\text m,\) \(4~\text s\)
2. \(0.004~\text m,\) \(\pi/2~\text s\)
3. \(80~\text m,\) \(\pi/2~\text s\)
4. \(80~\text m,\) \(4~\text s\)
\(y(x,t)=0.004 \text{sin}(80x-4t)\)
in which the numerical constants are in SI units. The amplitude and the time period of the wave are, respectively:
1. \(0.004~\text m,\) \(4~\text s\)
2. \(0.004~\text m,\) \(\pi/2~\text s\)
3. \(80~\text m,\) \(\pi/2~\text s\)
4. \(80~\text m,\) \(4~\text s\)
Subtopic: Wave Motion |
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Level 1: 80%+
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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: Wave Motion |
92%
Level 1: 80%+
JEE
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If the equation of a wave is represented by \(y=10^{-4} \sin \left(100 t-\frac{x}{10}\right) \text{m}\), then the velocity of the wave will be:
1. \(100~\text{m/s}\)
2. \(4~\text{m/s}\)
3. \(1000~\text{m/s}\)
4. \(0\)
1. \(100~\text{m/s}\)
2. \(4~\text{m/s}\)
3. \(1000~\text{m/s}\)
4. \(0\)
Subtopic: Wave Motion |
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When sound wave is refracted from air to water, which of the following will remain unchanged?
1. Wave number
2. Wavelength
3. Wave velocity
4. Frequency
Subtopic: Wave Motion |
90%
Level 1: 80%+
Hints
The equation \(y=A \text{cos}(kx-\omega t )\) represents a wave motion with:
| 1. | amplitude \(A\), frequency \(\dfrac{\omega}{2\pi}\) |
| 2. | amplitude \(\dfrac{A}{2}\), frequency \(\dfrac{2\omega}{\pi}\) |
| 3. | amplitude \(2A,\) frequency \(\dfrac{\omega}{4\pi}\) |
| 4. | does not represent a wave motion |
Subtopic: Wave Motion |
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A waveform propagating along the \(x\)-axis is given by:
\(y(x,t)=3~\text{mm}\sin2\pi\big[(100~\text s^{-1})t+(20~\text m^{-1})x\big].\) The speed of the wave is:
1. \(0.03~\text{mm/s}\)
2. \(5~\text{m/s}\)
3. \(0.02~\text{m/s}\)
4. \(60~\text{m/s}\)
\(y(x,t)=3~\text{mm}\sin2\pi\big[(100~\text s^{-1})t+(20~\text m^{-1})x\big].\) The speed of the wave is:
1. \(0.03~\text{mm/s}\)
2. \(5~\text{m/s}\)
3. \(0.02~\text{m/s}\)
4. \(60~\text{m/s}\)
Subtopic: Wave Motion |
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Level 1: 80%+
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If the equation of a wave is represented by: \(y=10^{-4}~ \mathrm{sin}\left(100t-\dfrac{x}{10}\right)~\text m,\) where \(x \) is in meters and \(t\) in seconds, then the velocity of the wave will be:
| 1. | \(100\) m/s | 2. | \(4\) m/s |
| 3. | \(1000\) m/s | 4. | \(0\) m/s |
Subtopic: Wave Motion |
89%
Level 1: 80%+
AIPMT - 2001
Hints
Which of the following expressions represents a wave?
| 1. | \(y=A \sin (\omega t-kx)\) |
| 2. | \(y=A \cos ^2(a t-bx+c)+A \sin ^2(at-bx+c)\) |
| 3. | \(y=A \sin kx\) |
| 4. | \(y=A \sin \omega t\) |
Subtopic: Wave Motion |
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Level 1: 80%+
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Match the terms in Column-I with their corresponding descriptions in Column-II based on their relationship to wave phenomena.
Codes:
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | Wavelength \((\lambda)\) | \(\mathrm{(P)}\) | \(v=\lambda\times f\) |
| \(\mathrm{(B)}\) | Frequency \((f)\) | \(\mathrm{(Q)}\) | maximum displacement from the equilibrium position |
| \(\mathrm{(C)}\) | Amplitude \((A)\) | \(\mathrm{(R)}\) | number of oscillations per second |
| \(\mathrm{(D)}\) | Speed of a wave \((v)\) | \(\mathrm{(S)}\) | inversely proportional to frequency |
| 1. | \(\mathrm{A\text- Q,B\text- P,C\text- S,D\text-R }\) |
| 2. | \(\mathrm{A\text-S ,B\text-R ,C\text-Q ,D\text-P }\) |
| 3. | \(\mathrm{A\text-Q ,B\text-R ,C\text-S ,D\text-P }\) |
| 4. | \(\mathrm{A\text- S,B\text-Q ,C\text-P ,D\text- R}\) |
Subtopic: Wave Motion |
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Level 1: 80%+
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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%
Level 1: 80%+
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