Inverse Square Law for Acoustics

The intensity of a sound is proportional to the square of its sound pressure $p$ , where pressure is force per unit area

Therefore, the average intensity at distance $r_{12}$ away from a point source of average-intensity

$$I_1\propto\left<\left\vert p_1\right\vert^2\right>$$   is$$\qquad \zbox{I(\mathbf{x}_2) = \frac{I_1}{r_{12}^2}}$$

This is a so-called inverse square law.

Remember that far away (in wavelengths) 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: