The transverse displacement of a string (clamped at both ends) is given by;
\(y(x,t)=0.06\sin\Big(\dfrac{2\pi}{3}x\Big)\cos(120\pi t)\)
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

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is $3.5\times {10}^{-2}$ kg and its linear mass density is$4.0\times {10}^{-2}$   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

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

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

A traveling harmonic wave on a string is described by \(y(x,t) = 7.5 ~\mathrm{sin}(0.0050x+12t+\frac{\pi}{4})\). What is the displacement of oscillation of a point at \(x=1 ~\text{cm}\) and \(t=1~\text{s}\)? (\(\sin(12.79)=0.22\))
1. \(1.66~\text{cm}\)
2. \(1.54~\text{cm}\)
3. \(1.39~\text{cm}\)
4. \(1.29~\text{cm}\)

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km/h. What is the frequency of sound reflected by the enemy submarine? (the speed of sound in water to be 1450 m/sec.)

(1) 44.2 kHz

(2) 45.9 kHz

(3) 43.7 kHz

(4) 46.1 kHz