Q. No.A steel wire has a length of \(12.0\) m and a mass of \(2.10\) kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air, at \(20^{\circ}\mathrm{C}\) (which is \(343\) m/s)?
1. \(4.3\times10^3\) N
2. \(3.2\times10^4\) N
3. \(2.06\times10^4\) N
4. \(1.2\times10^4\) N
1. \(4.3\times10^3\) N
2. \(3.2\times10^4\) N
3. \(2.06\times10^4\) N
4. \(1.2\times10^4\) N
The speed of sound in air is:
| 1. | dependent on pressure. |
| 2. | decreases with temperature. |
| 3. | independent of temperature. |
| 4. | increases with humidity. |
A bat emits an ultrasonic sound of frequency \(1000\) kHz in the air. If the sound meets a water surface, what is the wavelength of the reflected sound? (The speed of sound in air is \(340\) m/sec and in water is \(1486\) m/sec)
1. \(3.4 \times 10^{-4}~\text{m}\)
2. \(1 . 49 \times 10^{- 3} ~ \text{m}\)
3. \(2 . 34 \times 10^{- 2} ~\text{m}\)
4. \(1 . 73 \times10^{- 3} ~\text{m}\)
A bat emits an ultrasonic sound of frequency \(1000~\text{kHz}\) in the air. If the sound meets a water surface, what is the wavelength of the refracted sound?
(speed of sound in air is \(340~\mathrm{m/s}\) and in water \(1486~\mathrm{m/s}\))
| 1. | \(3.4 \times 10^{-4} \mathrm{~m} \) | 2. | \(1.4 \times 10^{-3} \mathrm{~m} \) |
| 3. | \(2.5 \times 10^{-4} \mathrm{~m} \) | 4. | \(1.8 \times 10^{-3} \mathrm{~m}\) |
A hospital uses an ultrasonic scanner to locate tumors in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is \(1.7~\text{km/s}\)? The operating frequency of the scanner is \(4.2~\text{MHz}\).
1. \(3.0 \times10^{-4}~\text{m}\)
2. \(4.0 \times10^{-4}~\text{m}\)
3. \(3.5 \times10^{-4}~\text{m}\)
4. \(2.0 \times10^{-4}~\text{m}\)
A transverse harmonic wave on a string is described by, \(y(x,t) = 3.0 ~\sin ( 36t + 0.018x + {\dfrac {\pi} 4})\) where \(x\) and \(y\) are in cm and \(t\) in sec. The positive direction of \(x\) is from left to right. What is the shortest distance between two successive crests in the wave?
| 1. | \(1.3\) m | 2. | \(3.0\) m |
| 3. | \(2.5\) m | 4. | \(3.5\) m |
For the travelling harmonic wave, \(y(x,t) = 2.0\ \text{cos}\ 2\pi (10t - 0.0080x + 0.35 )\) where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) is in seconds. The phase difference between the oscillatory motion of two points separated by a distance of \(4~\text{m}\) will be:
1. \(0.8 \pi\ \text{rad}\)
2. \(\pi\ \text{rad}\)
3. \(6.4\pi\ \text{rad}\)
4. \(4\pi\ \text{rad}\)
\(y(x,t)=0.06\sin\Big(\dfrac{2\pi}{3}x\Big)\cos(120\pi t)\)
where \(x\) and \(y\) are in metre and \(t\) in second. The length of the string is \(1.5\) m and its mass is \(3\times10^{-2}\) kg. The tension in the string is:
1. \(540\) N
2. \(648\) N
3. \(200\) N
4. \(425\) N
| 1. | a stationary wave |
| 2. | a travelling wave |
| 3. | both stationary and travelling wave |
| 4. | none of the above |
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is kg and its linear mass density is kg/m. What is the speed of the transverse wave on the string?
1. 74.31 m/s
2. 75.70 m/s
3. 78.75 m/s
4. 72 m/s
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