Question

A surface receiving sound is moved from its original position to a position three times farther away from the source of the sound. The intensity of the received sound thus becomes
a. three times as high,
b. nine times as high.
c. nine times as low.
d.three times as low.

Answer 1

Answer:

c. nine times as low.

Explanation:

Sound intensity is defined as the acoustic power transferred by a sound wave per unit of normal area to the direction of propagation:

$I\propto \frac{1}{A}$

Since the sound wave has a spherical wavefront of radius r, then the area is given by:

$A=4\pi r^2$

Here r is the distance from the source of the sound. Thus sound intensity decreases as:

$I\propto \frac{1}{4\pi r^2}\\\\I'\propto \frac{1}{4\pi r'^2}\\\\I'\propto \frac{1}{4\pi (3r)^2}\\\\I'\propto \frac{1}{9} \frac{1}{4\pi r^2}\\\\I'\propto \frac{1}{9} I$