Question

If the amplitude of a sound wave is tripled, by what factor will the intensity increase?

Answer 1

Answer:

By a factor 9

Explanation:

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

$I \propto A^2$

where

I is the intensity

A is the amplitude of the wave

In this problem, the amplitude of the sound wave is increased by a factor 3:

A' = 3A

So the intensity would change by

$I' \propto A'^2 = (3A)^2 = 9 A^2 = 9I$

So, the intensity would increase by a factor 9.