The Inverse-Square Law

Author: N.H. Crowhurst

Expansion of a sound wave

In the absence of any reverberation, the sound goes on outwards in an ever-expanding wave. The farther the wave goes from its starting point the larger its area becomes. The energy in the wave does not increase, because the wave can only pass on the original amount of energy put into it. This means the intensity in a square centimeter of the wave (which is how intensity is measured) must decrease as we go farther from the source. It is like spreading a fixed amount of butter on two slices of bread. If one slice is larger than the other, the butter on it will be thinner.

Doubling the distance means the area is quadrupled, so the intensity must be divided by four. Multiplying the distance by any number means that the area is increased by the square of that number, which, in turn, means that the intensity must be divided by the square of the number. This fact is known as the inverse-square law.

The inverse square law

The inverse-square law gives one reason why sound does not carry very far in the open air, unless there is something to make an echo. Cupping your hands or using a megaphone concentrates more of the original sound within a narrower angle, so that the power does not get scattered quite so widely. For this reason, the sound carries further in a particular direction. Because of reflection and reverberation effects, sound does not get "lost" so readily indoors.

Concentrating sound into narrower angle permits sound to carry further