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 \(20^{\circ}\text{C}\) (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. \(1 . 73 \times10^{- 3} ~\text{m}\)
(speed of sound in air is \(340~\text{m/s}\) and in water \(1486~\text{m/s}\))
| 1. | \(3.4 \times 10^{-4}~\text {m} \) | 2. | \(1.4 \times 10^{-3}~\text {m} \) |
| 3. | \(2.5 \times 10^{-4}~\text {m} \) | 4. | \(1.8 \times 10^{-3}~\text {m} \) |
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. | \(2.0 \times10^{-4}~\text{m}\) |
| 1. | \(1.3\) m | 2. | \(3.0\) m |
| 3. | \(2.5\) m | 4. | \(3.5\) m |
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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