The transverse displacement of a string (clamped at both ends) is given by

$y(x,t)=0.06\sin \left(\frac{2\pi }{3}x\right)\cos \left(120\pi t\right)$ 

where x and y are in m and t in sec. The length of the string is 1.5 m and its mass is $3\times {10}^{-2} kg$. The tension in the string is:

$$\begin{gathered} \left(1\right) 540 N \\ \left(2\right) 648 N \\ \left(3\right) 200 N \\ \left(4\right) 425 N \end{gathered}$$

$$\begin{gathered} y=2 \cos \left(3x\right) \sin \left(10t\right) represents: \\ \left(1\right) a stationary wave. \\ \left(2\right) a travelling wave. \\ \left(3\right) both stationary and travelling wave. \\ \left(4\right) none of the above. \end{gathered}$$

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 one-meter long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the minimum tube length is 25.5 cm. The speed of sound in air at the temperature of the experiment is: (The edge effects may be neglected.)

1. 324.16 m/s

2. 320 m/s

3. 345 m/s

4. 346.8 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 Hz beats. The tension in the string A is slightly reduced, and the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

1. 316 Hz

2. 318 Hz

3. 319 Hz

4. 314 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/sec?

(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 $y\left(x,t\right)=7.5\sin \left(0.0050x+12t+\frac{\pi }{4}\right)$.

What are the displacement of oscillation of a point at x = 1 cm and t = 1 sec?

(1) 1.66 cm

(2) 1.54 cm

(3) 1.39 cm

(4) 1.29 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