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 $Q$ is

• A. $3/2$
• B. $4/9$
• C. $2/3$
• D. $9/4$

Answer 1

The correct option is D

$9/4$

Step 1: Given data

Distance of a point $P$ from the source, $r_1=4m$

Distance of a point $Q$ from the source, $r_2=9m$

Step 2: Find the ratio of intensities, ${\mathit{I}}_{\mathbf{1}}\mathbf{/}{\mathit{I}}_{\mathbf{2}}$

For an isotropic point source of power, $P=I\left(4\pi r^2\right)$

The intensity $I$ at a distance $r$from it $=P/4\pi r^2$

Since power $P$ remains the same,

$$\begin{gathered} (I_1/I_2)={(r_2/r_1)}^2 \\ ={(9/4)}^2 \end{gathered}$$

Step 3: Find ratio of amplitudes, $A_{\mathbf{1}}\mathbf{/}{\mathit{A}}_{\mathbf{2}}$

$$\begin{gathered} A_1/{A_2}_{}=\surd (I_1/I_2) \\ =9/4 \end{gathered}$$

Hence, option (D) is correct.