A string with a mass \(2.50~\text{kg}\) is under a tension of \(200~\text{N}\). The length of the stretched string is \(20.0~\text{m}\). If the transverse jerk is struck at one end of the string, how long does it take for the disturbance to reach the other end?
1. \(0.5~\text{s}\)
2. \(0.6~\text{s}\)
3. \(0.4~\text{s}\)
4. \(0.1~\text{s}\)

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at \(20^{\circ}\mathrm{C}\) (which is  343 m/sec)?
1. $4.3\times {10}^3$ N
2. $3.2\times {10}^4$ N
3. $2.06\times {10}^4$ N
4. $1.2\times {10}^4$ N
 

A bat emits an ultrasonic sound of frequency 1000 kHz in the air. If the sound meets a water surface, what is the wavelength of the reflected sound? (The speed of sound in air is 340 m/sec and in water is 1486 m/sec)
1. \(3.4 \times 10^{-4}~\text{m}\)
2. \(1 . 49 \times 10^{- 3}  ~ \text{m}\)
3. \(2 . 34 \times 10^{- 2}   ~\text{m}\)
4. \(1 . 73 \times10^{- 3}   ~\text{m}\)

A transverse harmonic wave on a string is described by, \(y(x,t) = 3.0 sin ( 36t + 0.018x + {\pi \over 4})\) 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?

For the travelling harmonic wave, \(y(x,t) = 2.0\ cos\ 2\pi (10t - 0.0080x + 0.35 )\) where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) is in seconds. The phase difference between the oscillatory motion of two points separated by a distance of \(4~\text{m}\) will be:
1. \(0.8 \pi\ \text{rad}\)
2.  \(\pi\ \text{rad}\)
3. \(6.4\pi\ \text{rad}\)
4. \(4\pi\ \text{rad}\)

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

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 person standing between two parallel hills fires a gun and hears the first echo after ${\mathrm{t}}_1$ sec and the second echo after ${\mathrm{t}}_2$ sec. The distance between the two hills is: [Given: Speed of sound = v]

$1.$ $\frac{\mathrm{v}\left({\mathrm{t}}_1-{\mathrm{t}}_2\right)}{2}$
$2.$ $\frac{\mathrm{v}\left({\mathrm{t}}_1{\mathrm{t}}_2\right)}{2\left({\mathrm{t}}_1+{\mathrm{t}}_2\right)}$
$3.$ $\mathrm{v}\left({\mathrm{t}}_1+{\mathrm{t}}_2\right)$
$4.$ $\frac{\mathrm{v}\left({\mathrm{t}}_1+{\mathrm{t}}_2\right)}{2}$

A transverse wave moves from a medium \(A\) to a medium \(B\). In medium \(A\), the velocity of the transverse wave is \(500~\text{ms}^{-1}\) and the wavelength is \(5~\text{m}\). The frequency and the wavelength of the wave in medium \(B\) when its velocity is \(600~\text{ms}^{-1}\), respectively are:

A student tunes his guitar by striking a \(120~\text{Hz}\) with a tuning fork and playing the \(4^{th}\) string at the same time. By keen observation, he hears the amplitude of the combined sound oscillating thrice per second. Which of the following frequencies is most likely the frequency of the \(4^{th}\) string on his guitar?
1. \(130\)
2. \(117\)
3. \(110\)
4. \(120\)