#### Intensity

The intensity of a sound wave is its power/unit area.

I = P/A

In one dimension the intensity is constant as the wave travels.
In two or three dimensions, however, the intensity decreases as you get further from the source. In three dimensions, for a source emitting sound uniformly in all directions the intensity drops off as 1/r^{2}, where r is the distance from the source.

To understand the r dependence, surround the source by a sphere of radius r. All the sound, emitted by the source with power P, passes through the sphere. When the sound reaches the sphere its intensity is:

I = P/(4π r^{2})

That's the surface area of a sphere in the denominator.

Double the distance and the intensity drops by a factor of 4, etc.