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 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. \(425~\text{N}\)

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 \(100~\text{cm}\) 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

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