Q. No.A transverse harmonic wave on a string is described by, \(y(x,t) = 3.0 ~\sin \left(36t + 0.018x + {\dfrac {\pi} 4}\right)\) 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
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 meter and \(t\) in second. The length of the string is \(1.5~\text{m}\) and its mass is \(3\times10^{-2}~\text{kg}.\) The tension in the string is:
1. \(540~\text{N}\)
2. \(648~\text{N}\)
3. \(200~\text{N}\)
4. \(425~\text{N}\)
| 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 \(100~\text{cm}\) long is clamped at its middle. The fundamental frequency of the longitudinal vibrations of the rod is given to be \(2.53~\text{kHz}.\) What is the speed of sound in steel?
1. \(5.06~\text{km/s}\)
2. \(5.12~\text{km/s}\)
3. \(4.29~\text{km/s}\)
4. \(4.01~\text{km/s}\)
Two sitar strings, \(A\) and \(B,\) playing the note \(\mathrm{Ga},\) 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
A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/sec. What is the speed of sound for an observer standing on the station’s platform?
1. 332 m/s
2. 360 m/s
3. 344 m/s
4. 350 m/s
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