The phase difference between two waves, represented by
$\begin{array}{l}{\mathrm{y}}_1={10}^{-6}\sin \{100\mathrm{t}+(\mathrm{x}/50)+0.5\}\mathrm{m}\\ {\mathrm{y}}_2={10}^{-6}\cos \{100\mathrm{t}+\left(\frac{\mathrm{x}}{50}\right)\}\mathrm{m}\end{array}$
where X is expressed in metres and t is expressed in seconds, is approximate:
1. 2.07 radians
2. 0.5 radians
3. 1.5 radians
4. 1.07 radians

If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:

A point source emits sound equally in all directions in a non-absorbing medium. Two points, P and Q, are at distances of \(2\) m and \(3\) m, respectively, from the source. The ratio of the intensities of the waves at P and Q is:
1. \(3:2\)
2. \(2:3\)
3. \(9:4\)
4. \(4:9\)

A string is cut into three parts, having fundamental frequencies n₁, n₂, and n₃ respectively. The original fundamental frequency "n" is related by the expression:

1. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

2. $n=n_1\times n_2\times n_3$

3. $n=n_1+n_2+n_3$

4. $n=\frac{n_1+n_2+n_3}{3}$

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be:

1. 1%

2. 2%

3. 3%

4. 4%

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 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 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 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]

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