Question

As the distance of a sound wave from its source quadruples, how is the intensity changed? it increases by a factor of 4 it increases by a factor of 16 it decreases by a factor of 4 it decreases by a factor of 16

Answer 1

D. it decreases by a factor of 16

Answer 2

Answer:

it decreases by a factor of 16

Explanation:

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

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

where d is the distance.

Let's call d the initial distance. In this problem, the distance is then quadrupled, so the new distance is d' = 4 d. Substituting in the formula, we see that the new intensity is:

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

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