Question

How does the intensity of a sound wave change if the distance from the source is reduced by a factor of 3?

Answer 1

The intensity increases by a factor of 9

Answer 2

The intensity increases by a factor 9

Step-by-step explanation:

The intensity of a sound wave follows an inverse square law, that means that it is inversely proportional to the square of the distance:

`I\propto (1)/(r^2)`

where r is the distance from the source.

In this problem, the distance from the source is reduced by a factor 3, so the new distance is

`r'=(1)/(3)r`

this means that the new intensity will be

`I' \propto (1)/(r'^2)=(1)/(((1)/(3)r)^2)=9(1)/(r^2)=9I`

So, the intensity will increase by a factor 9.