Question

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

Answer 1

By a factor 9

Step-by-step 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.