Q. 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 4m and 9m 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) $\frac{9}{4}$
Explanation
(d) For an isotropic point source of power P, intensity I at a distance r from it is
$I = \frac{P}{4\pi r^{2}}$
$\therefore\frac{I_{1}}{I_{2}} = \left( \frac{r_{2}}{r_{1}} \right)^{2} = \left( \frac{9}{4} \right)^{2}$
Where A is the amplitude of a wave
$\therefore\frac{A_{1}}{A_{2}} = \sqrt{\frac{I_{1}}{I_{2}}} = \frac{9}{4}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.