Inverse Square Law for Acoustics

The intensity of a sound is proportional to the square of its sound pressure $p$.

Therefore, the average intensity at distance $r_{12}$ away from a point source of average-intensity $I_1\propto<\left\vert p_1\right\vert^2>$ is given by

$$I(\mathbf{x}_2) = \frac{I_1}{r_{12}^2}$$

This is a so-called inverse square law.

Remember that far away from a finite sound source,

• pressure falls off as $1/r$
• intensity falls off as $1/r^2$

where $r$ is the distance from the source.

Point-to-Point Spherical Pressure-Wave Simulation: