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Q. No.The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(300\) K is:
1.
\(\sqrt{\dfrac{2}{7}}\)
2.
\(\sqrt{\dfrac{1}{7}}\)
3.
\(\dfrac{\sqrt{3 }}{5}\)
4.
\(\dfrac{\sqrt{6 }}{5}\)
| 1. | \(\sqrt{\dfrac{2}{7}}\) | 2. | \(\sqrt{\dfrac{1}{7}}\) |
| 3. | \(\dfrac{\sqrt{3 }}{5}\) | 4. | \(\dfrac{\sqrt{6 }}{5}\) |
Subtopic: Speed of Sound |
Level 3: 35%-60%
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When sound waves produced under water emerge into the air, then:
| 1. | the frequency increases, and wavelength decreases. |
| 2. | the frequency remains constant, but the wavelength decreases. |
| 3. | the frequency decreases, wavelength remains constant. |
| 4. | the frequency remains constant but the wavelength increases. |
Subtopic: Speed of Sound |
Level 3: 35%-60%
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Given below are two statements:
| Statement I: | Sound waves travelling from air into water, incident obliquely, bend towards the normal. |
| Statement II: | Sound waves travel more slowly in water than in air. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Speed of Sound |
Level 3: 35%-60%
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The equation of vibration of a taut string, fixed at both ends, is given by: \(y=(4~\text{mm})~\cos\left(\dfrac{\pi x}{30~\text{cm}}\right)~\sin\Big(400\pi s^{-1}t\Big) \)
At which points is the amplitude equal to \(2\) mm?
At which points is the amplitude equal to \(2\) mm?
| 1. | \(x = \) \(10\) cm, \(20\) cm, \(30\) cm, \(40\) cm |
| 2. | \(x=\) \(10\) cm, \(15\) cm, \(30\) cm, \(45\) cm |
| 3. | \(x =\) \(10\) cm, \(20\) cm, \(40\) cm, \(80\) cm |
| 4. | \(x = \) \(10\) cm, \(20\) cm, \(40\) cm, \(50\) cm |
Subtopic: Standing Waves |
Level 3: 35%-60%
Hints
A string fixed at both ends is under tension \(T.\) It has a length \(L,\) and mass \(m.\) The fundamental frequency of the vibration is:
| 1. | \(\dfrac{ 1}{2L} \sqrt {\dfrac{T}{m}}\) | 2. | \(\dfrac{1}{4 L} \sqrt{\dfrac{T}{m}}\) |
| 3. | \(\dfrac{1}{2} \sqrt{\dfrac{TL}{2m}}\) | 4. | \(\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}\) |
Subtopic: Travelling Wave on String |
56%
Level 3: 35%-60%
Hints
The square of the speed of sound in a mono-atomic gas is proportional to:
| 1. | its internal energy |
| 2. | its internal energy per unit volume |
| 3. | its internal energy per unit mass |
| 4. | its internal energy per unit temperature |
Subtopic: Speed of Sound |
61%
Level 2: 60%+
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When a string vibrates in its second harmonic mode, at which point on the string is the motion maximal?
| 1. | One-quarter of the length away from an end. |
| 2. | In the middle, between the two ends. |
| 3. | One-third of the length away from an end. |
| 4. | The amplitude is the same at any point on the string. |
Subtopic: Travelling Wave on String |
60%
Level 2: 60%+
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Increasing the wave amplitude of a standing wave will:
| 1. | increase the number of nodes. |
| 2. | increase the number of antinodes. |
| 3. | increase the displacement of the cord at a node. |
| 4. | increase the displacement of the cord at an antinode. |
Subtopic: Standing Waves |
61%
Level 2: 60%+
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Suppose a string is \(20\) m long. Which of the following wavelengths is possible for standing waves on this string?
| 1. | \(3.5\) m | 2. | \(13.3\) m |
| 3. | \(30\) m | 4. | \(80\) m |
Subtopic: Standing Waves |
Level 3: 35%-60%
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The addition of two waves with slightly different frequencies results in the production of beats or a beat frequency. The result can be monitored using an oscilloscope. Consider the two figures shown below:
Keeping the lower frequency wave constant, we increase the frequency of the other wave. You would expect the display on the oscilloscope to go from:
Keeping the lower frequency wave constant, we increase the frequency of the other wave. You would expect the display on the oscilloscope to go from:
| 1. | Figure \(\mathrm I\) to Figure \(\mathrm{II}\). |
| 2. | Figure \(\mathrm{II}\) to Figure \(\mathrm{I}\). |
| 3. | There will not be a shift between Figure \(\mathrm{I}\) and Figure \(\mathrm{II}\), but the amplitude will increase. |
| 4. | There will not be a shift between Figure \(\mathrm{I}\) and Figure \(\mathrm{II}\), but the display will become brighter. |
Subtopic: Beats |
53%
Level 3: 35%-60%
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