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Q. No.The equation of vibration of a taut string, fixed at both ends, is given by; \(y=(3~\text{mm})~\text{cos}\left(\dfrac{\pi x}{10~\text{cm}}\right)~\text{sin}(800\pi~\text{s}^{-1}{t}).\) The positions of the nodes are:
1.
\(x= 0~\text{cm}, 10~\text{cm}, 20~\text{cm},....\)
2.
\(x= 0~\text{cm}, 20~\text{cm}, 40~\text{cm},....\)
3.
\(x= 5~\text{cm}, 10~\text{cm}, 15~\text{cm},....\)
4.
\(x= 5~\text{cm}, 15~\text{cm}, 25~\text{cm},....\)
Subtopic: Beats |
Level 4: Below 35%
Hints
Sinusoidal sound waves of the same frequency travelling in air along the \(x\)-axis and the \(y\)-axis arrive in phase with each other at the origin. Their amplitudes are equal to \(A\) (each). The amplitude of the vibration at the origin is:
| 1. | \(A\) | 2. | \(\sqrt 2A\) |
| 3. | \(2A\) | 4. | \((2+\sqrt2)A\) |
Subtopic: Wave Motion |
Level 4: Below 35%
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 |
60%
Level 2: 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 |
58%
Level 3: 35%-60%
Hints
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
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%
Hints
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. | \(\dfrac{\sqrt{6 }}{5}\) |
Subtopic: Speed of Sound |
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
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%
Hints
When two identical loudspeakers playing the same frequency are placed equidistant from an observer, a sound of \(60\) dB is heard if the sources are in phase with each other. However, if the two speakers are out of phase, no sound is heard. If the speakers are played with a phase difference of \(90^\circ,\) the sound heard will be:
1. \(30\sqrt2 \) dB
2. \((60+\sqrt2) \) dB
3. \(57\) dB
4. \(60\sqrt2 \) dB
1. \(30\sqrt2 \) dB
2. \((60+\sqrt2) \) dB
3. \(57\) dB
4. \(60\sqrt2 \) dB
Subtopic: Pressure Wave in Sound |
Level 4: Below 35%
Hints
A heavy uniform rope \(PQ\) is suspended from the ceiling. The lowest end of the rope is given a sharp transverse "shake" (or vibration) so as to cause a pulse. This pulse travels upward. As it travels upward, its speed:
| 1. | increases | 2. | decreases |
| 3. | first increases and then decreases | 4. | remains constant |
Subtopic: Travelling Wave on String |
58%
Level 3: 35%-60%
Hints
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