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