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

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

NTA AbhyasNTA Abhyas 2022

Solution:

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