Answer:
The intensity decreases by a factor 16
Explanation:
The intensity of a sound wave is inversely proportional to the square of the distance:
[tex]I \propto \frac{1}{d^2}[/tex]
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:
[tex]I' \propto \frac{1}{d'^2}=\frac{1}{(4d)^2}=\frac{1}{16 d^2}=\frac{I}{16}[/tex]
so, we see that the intensity has decreased by a factor 16.
