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Q. No.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?
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 |
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A waveform given by: \(y=3A\sin(\omega t-kx)\)
is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
| 1. | \(7A\) | 2. | \(A\) |
| 3. | \(3.5A\) | 4. | \(5A\) |
Subtopic: Wave Motion |
86%
From NCERT
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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 |
From NCERT
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Given below are two statements:
| Statement I: | The speed of sound waves in a medium depends on the elastic modulus and the density of the medium. |
| Statement II: | The speed of sound in a gas is independent of its temperature. |
| 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 |
72%
From NCERT
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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 |
From NCERT
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The first overtone of a closed pipe has a frequency \(f_c.\) A frequency that is \(2f_c\) can be excited from an open pipe of the same length but vibrating in its:
| 1. | \(2^{\text{nd}}\) harmonic | 2. | \(3^{\text{rd}}\) harmonic |
| 3. | \(6^{\text{th}}\) harmonic | 4. | \(12^{\text{th}}\) harmonic |
Subtopic: Standing Waves |
67%
From NCERT
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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. \(\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}\)
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 |
57%
From NCERT
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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 |
58%
From NCERT
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The fundamental frequencies of a closed pipe and an open pipe are identical. The first overtone for the closed pipe is \(f_c\) and for the open pipe is \(f_o.\) Their ratio \(\dfrac{f_c}{f_o}\) is:
| 1. | \(1\) | 2. | \(1/2\) |
| 3. | \(2/3\) | 4. | \(3/2\) |
Subtopic: Standing Waves |
70%
From NCERT
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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. \((2+\sqrt2)A\)
1. \(A\)
2. \(\sqrt 2A\)
3. \(2A\)
4. \((2+\sqrt2)A\)
Subtopic: Wave Motion |
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