Q. No.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
(The edge effects may be neglected.)
1. \(324.16~\text{m/s}\)
2. \(320~\text{m/s}\)
3. \(345~\text{m/s}\)
4. \(346.8~\text{m/s}\)
A steel rod \(100\) cm long is clamped at its middle. The fundamental frequency of the longitudinal vibrations of the rod is given to be \(2.53\) kHz. What is the speed of sound in steel?
1. \(5.06\) km/s
2. \(5.12\) km/s
3. \(4.29\) km/s
4. \(4.01\) km/s
Two sitar strings, \(A\) and \(B,\) playing the note \(Ga,\) are slightly out of tune and produce \(6~\text{Hz}\) beats. The tension in the string \(A\) is slightly reduced, and the beat frequency is found to be reduced to \(3~\text{Hz}\). If the original frequency of \(A\) is \(324~\text{Hz}\), what is the frequency of \(B\)?
1. \(316~\text{Hz}\)
2. \(318~\text{Hz}\)
3. \(319~\text{Hz}\)
4. \(314~\text{Hz}\)
A train, standing at the outer signal of a railway station blows a whistle of frequency \(400\) Hz in still air. What is the frequency of the whistle for a platform observer when the train approaches the platform with a speed of \(10\) m/s?
(Speed of sound\(=340\) m/s)
1. \(512 \) Hz
2. \(312 \) Hz
3. \(412\) Hz
4. \(400\) Hz
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