# Inverse Square

A relationship in which a quantity is related to the reciprocal of the square of a second quantity.

Graph of y=1/x^{2}

### Acoustics

Under far field/free field conditions, sound intensity varies inversely with the square of the distance from the source. In pure spherical divergence of sound from a point source in free space, the sound pressure level decreases 6 dB for each doubling of the distance.

At distances large compared to the size of the source, sound intensity diminishes according to the inverse square law.

This is relatively simple to reliably calculate, provided the source is small and outdoors where no echoes occur. In a reverberant sound field the calculation is more complex.

If the noise source is outdoors and its dimensions are small compared with the distance to the monitoring position (ideally a point source), then as the sound energy is radiated it will spread over an area which is proportional to the square of the distance. This is an 'inverse square law' where the sound level will decline by 6dB for each doubling of distance.

**See also: **Distance Double Law, Inverse Proportionality, Sound Propagation, Spherical Divergence.

**Subjects: ** Mathematics