A man drops a stone into a lake from the top of a tower that is \(500~\text{m}\) high. If the speed of sound in air is \(340~\text{m/s},\) approximately how long after releasing the stone will he hear the sound of the splash? \(\left(\text{take }g=10~\text{m/s}^2\right)\)
1. \(11.5~\text{s}\)
2. \(21~\text{s}\)
3. \(10~\text{s}\)
4. \(14~\text{s}\)

A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at a distance of 2m and 3m respectively from the source. The ratio of the intensities of the waves at P and Q is :

(1) 9 : 4

(2) 2 : 3

(3) 3 : 2

(4) 4 : 9

If the pressure amplitude in a sound wave is tripled, then the intensity of sound is increased by a factor of

(1) 9

(2) 3

(3) 6

(4) $\sqrt{3}$

The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is $y_1=A\sin (\pi x/L)\sin \omega t$ and energy is E₁, and in another experiment its displacement is $y_2=A\sin (2\pi x/L)\sin 2\omega t$ and energy is E₂. Then :

(1) E₂ = E₁

(2) E₂ = 2E₁

(3) E₂ = 4E₁

(4) E₂ = 16E₁

Consider ten identical sources of sound all giving the same frequency but having phase angles which are random. If the average intensity of each source is I₀, the average of resultant intensity I due to all these ten sources will be :

(1) I = 100 I₀

(2) I = 10 I₀

(3) I = I₀

(4) $I=\sqrt{10}{I}_0$

Two identical pulses in a stretched string, initially \(8\) cm apart, are moving toward each other as shown in the figure. The speed of each pulse is \(2\) cm/s. What will be the total energy of the pulses after \(2~\text{s}\text{?}\)

1. Zero
2. Purely kinetic
3. Purely potential
4. Partly kinetic and partly potential

The displacement-time graphs for two sound waves A and B are shown in the figure, then the ratio of their intensities I_A/I_B is equal to :

1. 1 : 4

2. 1 : 16

3. 1 : 2

4. 1 : 1

Two pulses is a stretch string whose centers are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s . After 2 seconds, the total energy of the pulses will be:

1.  zero

2.  Purely kinetic

3.  Purely potential

4.  Partly kinetic and partly potential 

Two wave trains, with intensities I and 2I respectively arrive and superpose at a point P in opposite phases. The amplitude of the superposed wave at P at that instant will be proportional to,

1. $\sqrt{3I}$

2. $\sqrt{I}$

3. $\sqrt{\left(3-2\sqrt{2}\right)I}$

4. $\left(\sqrt{2}+1\right)\sqrt{I}$

Assertion: In a stationary wave, there is no transfer to energy.

Reason: There is no outward motion of the disturbance from one particle to adjoining particle in a stationary wave.