Question

As the distance of a sound wave from its source quadruples, how is the intensity changed?

Answer 1

Answer:

The intensity decreases by a factor 16

Explanation:

The intensity of a sound wave is inversely proportional to the square of the distance:

$I \propto \frac{1}{d^2}$

where

I is the intensity

d is the distance from the sound source

In this problem, we have that the distance from the source is quadrupled:

d' = 4 d

So, the new intensity will be:

$I' \propto \frac{1}{d'^2}=\frac{1}{(4d)^2}=\frac{1}{16 d^2}=\frac{I}{16}$

so, we see that the intensity has decreased by a factor 16.

Answer 2

d. it decreases by a factor of 16