Question

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

• A. 9:04
• B. 2:03
• C. 3:02
• D. 4:09

Answer 1

Answer: (A)

9:04

Answer 2

The average power per unit area that is incident perpendicular to the direction of propagation is called the intensity ie, $I=\frac{P}{4 \pi r^{2}}$ or $I \propto \frac{1}{r^{2}}$ or $\frac{I_{1}}{I_{2}}=\left(\frac{r_{2}}{r_{1}}\right)^{2}$ Here, $r_{1}=2 \,m, r_{2}=3 \,m$ $\therefore \frac{I_{1}}{I_{2}}=\left(\frac{3}{2}\right)^{2}=\frac{9}{4}$