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Q. No.Two waves executing simple harmonic motion travelling in the same direction with the same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt 3 \) times of amplitude of individual motions. The phase difference between the two motions is:
1.
\(30^{\circ}\)
2.
\(45^{\circ}\)
3.
\(60^{\circ}\)
4.
\(90^{\circ}\)
Subtopic: Standing Waves |
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A wire of length \(30\) cm, stretched between rigid supports, has its \(\mathrm{n}\)th and \(\mathrm{(n+1)}\)th harmonics at \(400\) Hz and \(450\) Hz, respectively. If the tension in the string is \(2700\) N, its linear mass density is:
| 1. | \(3\) kg/m | 2. | \(6\) kg/m |
| 3. | \(9\) kg/m | 4. | \(1\) kg/m |
Subtopic: Standing Waves |
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In the wave equation, \({y}=0.5 \sin \dfrac{2 \pi}{\lambda}(400 {t}-{x}) ~{\text m}, \) the velocity of the wave will be:
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
Subtopic: Wave Motion |
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A longitudinal wave is represented by \(x = 10 ~\sin ~2 \pi \left( nt- {\dfrac x \lambda}\right)\) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:
| 1. | \(2 \pi\) cm | 2. | \(5 \pi\) cm |
| 3. | \(\pi\) cm | 4. | \({\dfrac {5 \pi} 2}\) cm |
Subtopic: Wave Motion |
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A metallic wire with mass per unit length \(6\times 10^{-3}~\text{kg/m}\) is under the tension of \(60~\text N.\) What is the speed of transverse wave in the wire?
| 1. | \(100~\text{m/s}\) | 2. | \(500~\text{m/s}\) |
| 3. | \(600~\text{m/s}\) | 4. | \(10,000~\text{m/s}\) |
Subtopic: Travelling Wave on String |
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A wave traveling along a string is described by;
\(y(x,t)=0.004 \text{sin}(80x-4t)\)
in which the numerical constants are in SI units. The amplitude and the time period of the wave are, respectively:
1. \(0.004~\text m,\) \(4~\text s\)
2. \(0.004~\text m,\) \(\pi/2~\text s\)
3. \(80~\text m,\) \(\pi/2~\text s\)
4. \(80~\text m,\) \(4~\text s\)
\(y(x,t)=0.004 \text{sin}(80x-4t)\)
in which the numerical constants are in SI units. The amplitude and the time period of the wave are, respectively:
1. \(0.004~\text m,\) \(4~\text s\)
2. \(0.004~\text m,\) \(\pi/2~\text s\)
3. \(80~\text m,\) \(\pi/2~\text s\)
4. \(80~\text m,\) \(4~\text s\)
Subtopic: Wave Motion |
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The speed of the sound at \(0 ~^\circ\text{C}\) is nearly \(330~\text{m/s}.\) For a frequency of \(200~\text{Hz}\) the wavelength is:
1. \(1.0~\text m\)
2. \(1.5~\text m\)
3. \(1.65~\text m\)
4. \(1.75~\text m\)
1. \(1.0~\text m\)
2. \(1.5~\text m\)
3. \(1.65~\text m\)
4. \(1.75~\text m\)
Subtopic: Speed of Sound |
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A pipe of length \(11~\text{cm}\) is closed at one end. The first harmonic frequency of the pipe in the air at \(0^\circ \text{C}\) is:
(the velocity of sound at \(0^\circ \text{C}=330~\text{m/s}\))
1. \(1200~\text{Hz}\)
2. \(1000~\text{Hz}\)
3. \(800~\text{Hz}\)
4. \(750~\text{Hz}\)
(the velocity of sound at \(0^\circ \text{C}=330~\text{m/s}\))
1. \(1200~\text{Hz}\)
2. \(1000~\text{Hz}\)
3. \(800~\text{Hz}\)
4. \(750~\text{Hz}\)
Subtopic: Standing Waves |
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A pipe is \(15\) cm long and is open at both ends. Which harmonic mode of the pipe will resonate with a \(2.2\) kHz sound source?
(Given: the velocity of sound in air \(=330\) m/s)
| 1. | fundamental | 2. | second harmonic |
| 3. | third harmonic | 4. | fourth harmonic |
Subtopic: Standing Waves |
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A point source of sound is placed in a non-absorbing medium. Two points \(A\) and \(B\) are at a distance of \(2~\text m\) and \(3~\text m\) from the source, respectively. The ratio of the intensity of the wave at \(A\) to that at \(B\) is:
1. \(\sqrt 3:\sqrt 2\)
2. \(3:2\)
3. \(9:4\)
4. \(2:3\)
1. \(\sqrt 3:\sqrt 2\)
2. \(3:2\)
3. \(9:4\)
4. \(2:3\)
Subtopic: Energy of Waves |
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