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

it decreases by a factor of 16

Step-by-step explanation:

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

`I\propto (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 (1)/((d')^2)=(1)/((4d)^2)=(1)/(16) (1)/(d^2)=(I)/(16)`

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