The intensity of sound from an isotropic point
source decreases with the square of the distance from the source.
A point sound source emits sound isotropically, that
is with equal intensity in all directions. The intensity I from a point source as a function of the distance
r from the point source can be found easily.
Imagine a sphere with a radius r and centered at the
source S. All the energy emitted by the source must pass
through the imaginary sphere. Since the source is isotropic, the energy is
distributed equally over the imaginary sphere. Thus, the intensity at
distance r from the source is equal to the average power of the source Ps
divided by the area of the imaginary sphere 4pr2.