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 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 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]

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

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 string of length l is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:

1. 1:2:3: ......

2. 1:3:5:7: ......

3. 1:2:4:8: ..........

4. 1:3:9: ........

Given the equation for a wave on the string, y = 0.5 sin(5x - 3t) where y and x are in metres and t in seconds, the ratio of the maximum speed of particle to the speed of wave is:

1. 1:1

2. 5:2

3. 3:2

4. 4:5

Two sound waves given by the equations \(y=A\sin 122 \pi t\) and \(y=A\sin 128 \pi t\) pass through a point simultaneously. The number of beats per second is:

The equation of a stationary wave is given as $\mathrm{y}=\mathrm{A}$ $\sin$ $0.5\mathrm{\pi t}$ $\cos (0.2\mathrm{\pi x}),$ $$ where t is in seconds and x in centimetres. Which of the following is correct?

A cylindrical tube open at both ends has a fundamental frequency f₀ in the air. The tube is dipped vertically in water such that half its length is inside water. The fundamental frequency of the air column now will be:

1. $\frac{3f_{\mathit{0}}}{4}$

2. $f_0$

3. $\frac{f_{\mathit{0}}}{2}$

4. 2$f_0$