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Q. No.When a sound wave travels from air into water (or vice-versa), then:
1.
its frequency changes
2.
its wavelength changes
3.
both frequency and wavelength change
4.
both frequency and wavelength remain unchanged
Subtopic: Types of Waves |
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Level 2: 60%+
Hints
For the wave equation, \(y=A\sin(Bt-Cx)\) , match Column I with Column II:
Codes:
| Column I | Column II | ||
| (a) | Wave speed | (p) | \(\large\frac{B}{2\pi}\) |
| (b) | Maximum particle speed | (q) | \(\large\frac{C}{2\pi}\) |
| (c) | Wave frequency | (r) | \(\large\frac{B}{C}\) |
| (d) | Wavelength | (s) | None of these |
Codes:
| 1. | a - s, b - p, c - q, d - r |
| 2. | a - r, b - p, c - q, d - s |
| 3. | a - s, b - q, c - p, d - r |
| 4. | a - r, b - s, c - p, d - s |
Subtopic: Wave Motion |
81%
Level 1: 80%+
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Hints
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A tuning fork, placed in a room, vibrates according to the equation: \(Y=(10^{-4}~\text m)\sin\Big({\large\frac{2\pi t}{0.01~\text s}}\Big) \) where \(Y\) is the displacement of the tip of a prong. The speed of sound in air is \(330~\text{m/s.}\) The amplitude of vibration of the prong is:
1. \(10^{-4}~\text{m}\)
2. \(2\times10^{-4}~\text{m}\)
3. \(10^{-6}~\text{m}\)
4. \(2\times10^{-6}~\text{m}\)
1. \(10^{-4}~\text{m}\)
2. \(2\times10^{-4}~\text{m}\)
3. \(10^{-6}~\text{m}\)
4. \(2\times10^{-6}~\text{m}\)
Subtopic: Wave Motion |
85%
Level 1: 80%+
Hints
A tuning fork, placed in a room, vibrates according to the equation: \(Y=(10^{-4}~\text m)\sin\Big({\large\frac{2\pi t}{0.01~\text s}}\Big)\) where \(Y\) is the displacement of the tip of a prong. The speed of sound in air is \(330~\text{m/s}.\)
If an additional tuning fork of frequency \(102~\text{Hz}\) is sounded together with this, then a beat frequency of:
If an additional tuning fork of frequency \(102~\text{Hz}\) is sounded together with this, then a beat frequency of:
| 1. | \(1~\text{Hz}\) will be heard. |
| 2. | \(2~\text{Hz}\) will be heard. |
| 3. | \(202~\text{Hz}\) will be heard. |
| 4. | \(101~\text{Hz}\) will be heard. |
Subtopic: Beats |
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Level 1: 80%+
Hints
A taut string, fixed at both ends, is allowed to vibrate in its fundamental mode with a maximum amplitude \(A.\) The total energy of vibration is proportional to:
| 1. | \(A\) | 2. | \(A^2\) |
| 3. | \(A^4\) | 4. | \(\dfrac{1}{A^2}\) |
Subtopic: Energy of Waves |
88%
Level 1: 80%+
Hints
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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The first two lengths of an air column, in a resonance column method, were found to be \(23.2 \mathrm{~cm} \) and \(76.4\mathrm{~cm}\) respectively. The end correction for the tube is:
1. \(4.2 \mathrm{~cm} \)
2. \(1.7 \mathrm{~cm}\)
3. \(3.4 \mathrm{~cm}\)
4. \(6.8 \mathrm{~cm}\)
1. \(4.2 \mathrm{~cm} \)
2. \(1.7 \mathrm{~cm}\)
3. \(3.4 \mathrm{~cm}\)
4. \(6.8 \mathrm{~cm}\)
Subtopic: Standing Waves |
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Level 2: 60%+
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Hints
An open organ pipe of length \(L_1\) is in resonance with a closed pipe of length \(L_2;\) both are vibrating in their fundamental modes. Then:
1. \(L_1=2L_2\)
2. \(L_2=2L_1\)
3. \(L_1=4L_2\)
4. \(L_2=4L_1\)
1. \(L_1=2L_2\)
2. \(L_2=2L_1\)
3. \(L_1=4L_2\)
4. \(L_2=4L_1\)
Subtopic: Standing Waves |
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Level 1: 80%+
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A sinusoidal waveform whose displacement is given by:
\(y(x,t)=(5~\text{mm})\sin2\pi\)\(\large{\Big(\frac{x}{2~\text{m}}+\frac{t}{0.01~\text s}\Big)}\)
propagates along the \(x\)-axis. The wavelength of the waveform is:
\(y(x,t)=(5~\text{mm})\sin2\pi\)\(\large{\Big(\frac{x}{2~\text{m}}+\frac{t}{0.01~\text s}\Big)}\)
propagates along the \(x\)-axis. The wavelength of the waveform is:
| 1. | \(\large\frac{2\pi}{2}\)\(~\text m\) | 2. | \(\large\frac{1}{2}\)\(~\text m\) |
| 3. | \(\large\frac{2}{2\pi}\)\(~\text m\) | 4. | \(2~\text m\) |
Subtopic: Wave Motion |
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Level 1: 80%+
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A string, under tension, and lying along the \(x\)-axis is set into transverse vibrations. The displacement at a point \(x\) is given by the function \(y(x,t)\) where \(t\) represents the time: \(y(x,t)=\left ( 3~\text{mm} \right )\mathrm{sin}\left ( \frac{\pi x}{20~\text{cm}} \right ) \)\(\mathrm{cos}\left\{2\pi\left ( 100~\text{s}^{-1} \right )t \right\}\)
The maximum amplitude of vibration at any point on the string is:
1. \(3~\text{mm}\)
2. \(20~\text{cm}\)
3. \(300~\text{mm}\)
4. \(15~\text{mm}\)
The maximum amplitude of vibration at any point on the string is:
1. \(3~\text{mm}\)
2. \(20~\text{cm}\)
3. \(300~\text{mm}\)
4. \(15~\text{mm}\)
Subtopic: Standing Waves |
85%
Level 1: 80%+
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