Question

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 $Q$ if

• A. $\frac{3}{2}$
• B. $\frac{4}{9}$
• C. $\frac{2}{3}$
• D. $\frac{9}{4}$

Answer 1

Answer: (D)

$\frac{9}{4}$

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,
$\therefore$ $\frac{I_1}{I_2}=(\frac{r_2}{r_1}{)}^2$
$=(\frac{9}{4}{)}^2$
$\because I\alpha A^2$
Where A is the amplitude of a wave
$\therefore \frac{A_1}{A_2}=\sqrt{\frac{I_1}{I_2}}$
$=\frac{9}{4}$