Question

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at distances of $2m$ and $3m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is

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

Answer 1

The correct option is A

$9:4$

Step 1: Given data

Distance from source from $P$, $r_1=2m$

Distance from source from $Q$, $r_2=3m$

Step 2: Find the ratio of the intensity of the waves

Intensity, $I$ is the rate at which light spreads over a surface of a given area some distance from a source. The intensity varies with the distance from the source and the power of the source.

$I=\frac{P}{4\pi r^2}$

Where,

$P=$Power

$r=$distance from source

$$\begin{gathered} I\propto \frac{1}{r^2} \\ \frac{I_1}{I_2}=\frac{r_2^2}{r_1^2} \\ \frac{I_1}{I_2}=\frac{9}{4} \end{gathered}$$ [Where, $I_1,I_2$ are the intensities of the waves at $P$ and $Q$]

Hence, option $\left(A\right)$ is correct.