Question

A point source emits sound equally in all directions in a non-absorbing medium. Two point 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. $9 : 4$
• B. $2:3$
• C. $3:2$
• D. $4 : 9$

Answer 1

Answer: (A)

$9 : 4$

Answer 2

Intensity $= \frac{energy}{time \times area}=\frac{power}{area}$ From a point source energy spread over the surfaceof sphere of radius $r$ $\therefore$ Intensity $I=\frac{P}{A}=\frac{P}{4\pi r^{2}}\propto\frac{1}{r^{2}}$ $\frac{I_{1}}{I_{2}}=\left(\frac{r_{2}}{r_{1}}\right)^{2}=\left(\frac{3}{2}\right)^{2}$ $\therefore \frac{I_{1}}{I_{2}}=\frac{9}{4}$