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

The intensity decreases by a factor 16

Explanation:

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

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:

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

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