The Inverse Square Law in Sound: Calculating Acoustic Distance Decay
The Inverse Square Law is a fundamental physical law governing the propagation of acoustic energy radiating from a point source in a three-dimensional free field.
Geometric Spherical Spreading
As a sound wave expands outward from a point source, its sound power \(W\) is distributed across an expanding spherical surface area \(A = 4\pi r^2\). Because the area scales with the square of the distance \(r\), acoustic intensity \(I\) decreases according to:
$$I = \frac{W}{4\pi r^2} \qquad \Delta L = 20 \log_{10}\left(\frac{d_1}{d_2}\right) \text{ dB}$$
Sound Intensity and Sound Pressure Level distance attenuation formulas
In practical terms, doubling the distance from a studio monitor in an anechoic free field results in an exact -6.02 dB drop in sound pressure level.
Model physical attenuation instantly using our Decibel Attenuation Calculator.
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