question_answer

A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source. The ratio of amplitudes of the waves at P and Q is

A) \[\frac{3}{2}\]                                   

B) \[\frac{4}{9}\]

C) \[\frac{2}{3}\]                   

D)        \[\frac{9}{4}\]

Correct Answer: D

Solution :

For an isotropic point source of power\[P\], intensity \[I\]at a distance r from it is                 \[I=\frac{P}{4\pi {{r}^{2}}}\] Since power\[P\]remains the same, \[\therefore \]  \[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}={{\left( \frac{9}{4} \right)}^{2}}\] where\[A\]is the amplitude of a wave \[\therefore \]  \[\frac{{{A}_{1}}}{{{A}_{2}}}=\sqrt{\frac{{{I}_{1}}}{{{I}_{2}}}}=\frac{9}{4}\]