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, \[\therefore \]  \[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}={{\left( \frac{9}{4} \right)}^{2}}\] \[\because \]                     \[I\propto {{A}^{2}}\] where A is the amplitude of a wave \[\therefore \]  \[\frac{{{A}_{1}}}{{{A}_{2}}}=\sqrt{\frac{{{I}_{1}}}{{{I}_{2}}}}=\frac{9}{4}\]