Q. No.A wave travelling in the positive \(x\)-direction having maximum displacement along \(y\)-direction as \(1~\text{m},\) wavelength \(2\pi~\text{m}\) and frequency of \(1/ \pi\) Hz is represented by:
1. \(y=\text{sin}(x-2t)\)
2. \(y=\text{sin}(2\pi x-2\pi t)\)
3. \(y=\text{sin}(10\pi x-20\pi t)\)
4. \(y=\text{sin}(2\pi x+2\pi t)\)
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\(y(x,t)=0.004 \text{sin}(80x-4t)\)
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. \(80~\text m,\) \(4~\text s\)
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
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
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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 |
\(y(x,t)=3~\text{mm}\sin2\pi\big[(100~\text s^{-1})t+(20~\text m^{-1})x\big].\) The speed of the wave is:
1. \(0.03~\text{mm/s}\)
2. \(5~\text{m/s}\)
3. \(0.02~\text{m/s}\)
4. \(60~\text{m/s}\)
| 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. | \(\mathrm{A\text- S,B\text-Q ,C\text-P ,D\text- R}\) |
| 1. | \(2 \pi\) cm | 2. | \(5 \pi\) cm |
| 3. | \(\pi\) cm | 4. | \({\dfrac {5 \pi} 2}\) cm |
A wave is represented by the equation \(y=(0.001~\text{mm})\sin[(50~\text{s}^{-1})t+(2.0~\text{m}^{-1})x].\)
| (a) | The wave velocity \(=100~\text{m s}^{-1}\). |
| (b) | The wavelength \(=2.0~\text{m}\). |
| (c) | The frequency \(=25/\pi~\text{Hz}\). |
| (d) | The amplitude \(=0.001~\text{mm}\). |
Choose the correct option:
| 1. | (a) and (b) |
| 2. | (b) and (c) |
| 3. | (c) and (d) |
| 4. | all of these |
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The given, equation describes a wave:
\(y=A~\text{sin}314\bigg[{\Large\frac{t}{0.5~\text s}}-{\Large\frac{x}{100~\text m}}\bigg].\)
Identify the correct relationships regarding its frequency \(n\) and wavelength \(\lambda.\)
(A) \(n = 2~\text{Hz}\)
(B) \(n = 100~\text{Hz}\)
(C) \(\lambda= 2~\text m\)
(D) \(\lambda= 100~\text m\)
Choose the correct option from the given ones:
| 1. | (A), (B) and (C) only |
| 2. | (A) and (B) only |
| 3. | (B) and (C) only |
| 4. | (B), (C) and (D) only |
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