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Q. No.The equation of a wave on a string of linear mass density \(0.04 \mathrm{~kg} \mathrm{~m}^{-1}\) is given by:
\({y}{=}{0}{.}{02}\left({m}\right)\sin\left[{{2}\mathit{\pi}\left({\frac{t}{{0}{.}{04}\left({s}\right)}{-}\frac{x}{{0}{.}{50}\left({m}\right)}}\right)}\right]\).
The tension in the string will be:
1.
\(4.0~\text{N}\)
2.
\(12.5~\text{N}\)
3.
\(0.5~\text{N}\)
4.
\(6.25~\text{N}\)
Subtopic: Travelling Wave on String |
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A \(100\) cm wire of mass \(40\) g is fixed at both ends. A tuning fork, vibrating at a frequency of \(50\) Hz, sets the wire into resonance in its fundamental mode. Then, the tension in the wire is:
1. \(400\) N
2. \(100\) N
3. \(25\) N
4. \(1600\) N
1. \(400\) N
2. \(100\) N
3. \(25\) N
4. \(1600\) N
Subtopic: Standing Waves |
69%
From NCERT
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If the absolute temperature increases by \(1\%\), the frequency of an organ pipe will:
1. increase by \(1\%\).
2. decrease by \(1\%\).
3. increase by \(0.5\%\).
4. decrease by \(0.5\%\).
1. increase by \(1\%\).
2. decrease by \(1\%\).
3. increase by \(0.5\%\).
4. decrease by \(0.5\%\).
Subtopic: Speed of Sound |
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From NCERT
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A pipe closed at one end produces a fundamental note of \(412\) Hz. It is cut into two pieces of equal length. The fundamental nodes produced by the two pieces are:
1. \(206\) Hz, \(412\) Hz
2. \(412\) Hz, \(824\) Hz
3. \(206\) Hz, \(824\) Hz
4. \(824\) Hz, \(1648\) Hz
1. \(206\) Hz, \(412\) Hz
2. \(412\) Hz, \(824\) Hz
3. \(206\) Hz, \(824\) Hz
4. \(824\) Hz, \(1648\) Hz
Subtopic: Standing Waves |
65%
From NCERT
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Two SHMs have equations:
\({x}_{1}{=}{a}\sin\left({\mathit{\omega}{t}{+}{\mathit{\phi}}_{1}}\right)\) and \({x}_{2}{=}{a}\sin\left({\mathit{\omega}{t}{+}{\mathit{\phi}}_{2}}\right)\).
If the amplitude of the resultant SHM is equal to amplitude of superimposing SHM(s), the phase difference between them is:
\({x}_{1}{=}{a}\sin\left({\mathit{\omega}{t}{+}{\mathit{\phi}}_{1}}\right)\) and \({x}_{2}{=}{a}\sin\left({\mathit{\omega}{t}{+}{\mathit{\phi}}_{2}}\right)\).
If the amplitude of the resultant SHM is equal to amplitude of superimposing SHM(s), the phase difference between them is:
| 1. | \(\frac{\mathit{\pi}}{6}\) | 2. | \(\frac{{2}\mathit{\pi}}{3}\) |
| 3. | \(\frac{\mathit{\pi}}{4}\) | 4. | \(\frac{\mathit{\pi}}{3}\) |
Subtopic: Wave Motion |
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A source of sound gives \(5\) beats per second when sounded with another source of frequency \(100\) per second. The second harmonic of the source, together with a source of frequency \(205\) per second, gives \(5\) beats per second. What is the frequency of the source?
1. \(95\) Hz
2. \(100\) Hz
3. \(105\) Hz
4. \(205\) Hz
1. \(95\) Hz
2. \(100\) Hz
3. \(105\) Hz
4. \(205\) Hz
Subtopic: Beats |
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The equation of vibration of a taut string, fixed at both ends, is given by:
\(y=(3~\text{mm})~\text{cos}\Big(\frac{\pi x}{10~\text{cm}}\Big)~\text{sin}(800\pi~\text{s}^{-1}~\text{t})\)
The speed of waves on the string is:
1. \(20\) m/s
2. 40 m/s
3. \(80\) m/s
4. \(160\) m/s
\(y=(3~\text{mm})~\text{cos}\Big(\frac{\pi x}{10~\text{cm}}\Big)~\text{sin}(800\pi~\text{s}^{-1}~\text{t})\)
The speed of waves on the string is:
1. \(20\) m/s
2. 40 m/s
3. \(80\) m/s
4. \(160\) m/s
Subtopic: Standing Waves |
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Given below are two statements:
| Assertion (A): | In a stationary wave, there is no transfer of energy. |
| Reason (R): | The ratio of kinetic energy to potential energy is independent of the position. |
| 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: Standing Waves |
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From NCERT
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Given below are two statements:
| Assertion (A): | The change in air pressure affects the speed of sound. |
| Reason (R): | The speed of sound in gases is proportional to the square of pressure. |
| 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. | Both (A) and (R) are false. |
Subtopic: Speed of Sound |
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Given below are two statements:
| Assertion (A): | Ocean waves hitting a beach are always found to be nearly normal to the shore. |
| Reason (R): | Ocean waves are longitudinal waves. |
| 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. | Both (A) and (R) are False. |
Subtopic: Types of Waves |
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