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Q. No.The equation of a wave on a string of linear mass density \(0.04~\text{kg m}^{-1}\) is given by:
\(y=(0.02~\text{m})\sin\left[{{2}\pi \left({\frac{t}{{0.04}~(\text{s})}-\frac{x}{{0.50}~(\text{m})}}\right)}\right].\) 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 |
79%
Level 2: 60%+
Hints
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 |
Subtopic: Standing Waves |
75%
Level 2: 60%+
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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 \(0.5\%\) |
Subtopic: Speed of Sound |
76%
Level 2: 60%+
Hints
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 |
68%
Level 2: 60%+
Hints
Two SHMs have equations:
\(x_{1}=a\sin\left({\omega t+\phi_{1}}\right)\) and \(x_2=a\sin\left({\omega t+\phi_2}\right)\).
If the amplitude of the resultant SHM is equal to amplitude of superimposing SHM(s), the phase difference between them is:
1. \(\dfrac{\mathit{\pi}}{6}\)
2. \(\dfrac{{2}\mathit{\pi}}{3}\)
3. \(\dfrac{\mathit{\pi}}{4}\)
4. \(\dfrac{\mathit{\pi}}{3}\)
\(x_{1}=a\sin\left({\omega t+\phi_{1}}\right)\) and \(x_2=a\sin\left({\omega t+\phi_2}\right)\).
If the amplitude of the resultant SHM is equal to amplitude of superimposing SHM(s), the phase difference between them is:
1. \(\dfrac{\mathit{\pi}}{6}\)
2. \(\dfrac{{2}\mathit{\pi}}{3}\)
3. \(\dfrac{\mathit{\pi}}{4}\)
4. \(\dfrac{\mathit{\pi}}{3}\)
Subtopic: Wave Motion |
76%
Level 2: 60%+
Hints
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. \(95~\text{Hz}\)
2. \(100~\text{Hz}\)
3. \(105~\text{Hz}\)
4. \(205~\text{Hz}\)
1. \(95~\text{Hz}\)
2. \(100~\text{Hz}\)
3. \(105~\text{Hz}\)
4. \(205~\text{Hz}\)
Subtopic: Beats |
86%
Level 1: 80%+
Hints
The equation of vibration of a taut string, fixed at both ends, is given by:
\(y=(3~\text{mm})~\text{cos}\Big(\dfrac{\pi x}{10~\text{cm}}\Big)~\text{sin}(800\pi~\text{s}^{-1}~\text{t})\)
The speed of waves on the string is:
1. \(20\) m/s
2. 40 m/s
3. \(80\) m/s
4. \(160\) m/s
\(y=(3~\text{mm})~\text{cos}\Big(\dfrac{\pi x}{10~\text{cm}}\Big)~\text{sin}(800\pi~\text{s}^{-1}~\text{t})\)
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 |
91%
Level 1: 80%+
Hints
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 |
61%
Level 2: 60%+
Hints
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 |
71%
Level 2: 60%+
Hints
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 |
56%
Level 3: 35%-60%
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