Rankers Physics

Waves and its Characteristics: Practice Problem & Solution

A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distance of $2text{ m}$ and $3text{ m}$ respectively from the source. The ratio of the intensities of the waves at P and Q is: (2005)
$9 : 4$
$2 : 9$
$9 : 2$
$4 : 9$

Solution Explained:

To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

For a point source in a non-absorbing medium, the intensity $I$ is inversely proportional to the square of the distance $r$ from the source ($I \propto 1/r^2$). Thus, $I_P/I_Q = (r_Q/r_P)^2 = (3/2)^2 = 9/4$.

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