Question

How does the intensity of a sound wave change if the distance from the
source is increased by a factor of 4?
A. The intensity decreases by a factor of 4.
B. The intensity increases to by a factor of 16.
c. The intensity decreases by a factor of 16.
D. The intensity increases by a factor of 4.

Answer 1

Answer:

The new intensity decreases by a factor of 16.

Explanation:

The intensity of sound wave is given by :

$I=\dfrac{P}{A}$

P is power

A is area

$I=\dfrac{P}{4\pi r^2}$

or

$I\propto \dfrac{1}{r^2}$, r is distance from the source

If the distance from the  source is increased by a factor of 4, r' = 4r

So,

$I'=\dfrac{1}{r'^2}\\\\I'=\dfrac{1}{(4r)^2}\\\\I'=\dfrac{1}{16}\times \dfrac{1}{r^2}\\\\I'=\dfrac{I}{16}$

So, the new intensity decreases by a factor of 16.