# Distance Attenuation

## What is Distance Attenuation?

Distance attenuation is defined as the way in which a sound level reduces as a listener moves away from a sound source. As sound travels from the source, the area over which the sound is spread increases like ripples on a pond. The way in which the skin of a balloon gets fainter as it is inflated is a good model for the way in which the sound level reduces as the distance and corresponding area increase. This means that the same amount of acoustic energy is dispersed over a greater area, and as a result the sound level at any position on this surface reduces as the distance from the source is increased.

Sound waves some distance from a small source on a hard ground surface with no nearby walls will disperse in a hemispherical pattern. If the source is suspended in the air it becomes a spherical distribution. In either case, the area of the (hemi)sphere is related to the square of the distance.

The area of a hemisphere is given by A = 2πr2, for a sphere it is A = 4πr2

In both cases this means that the area quadruples with every doubling of distance and increases by a factor of 100 if the distance is increased by a factor of 10. Acoustically, the sound level under these conditions reduces at a rate of 6dB for every doubling of distance from a source. However, after the original distance has been doubled, this increased distance then has to be doubled again (i.e. the original distance from the source has to be quadrupled in order to achieve a further 6dB reduction and then increased to 8 times the original distance for a further 6dB reduction). This also gives a 20dB reduction if the original separation distance is increased by a factor of 10.

Where sound is unable to disperse in this fashion, the reduction with distance is less, which is why the sound level indoors may not change once a listener is some distance from a source (depending upon other factors such as how reverberant or absorptive the room is).

For a line source, such as a road with continuous traffic passing along it, sound is dispersed in a cylindrical fashion along the length of the road. The area of a half-cylinder for a road length L is given by A = πrL. This means that the area over which the sound is dispersed is directly related to the separation distance, giving a reduction of 3dB for every doubling of distance from the source instead of 6dB for a point source.

If a listener is relatively close to a source it does not act like a ‘point source’ because the sound is dispersed over the entire area of the source. For example, a listener standing one metre from a large wall will be one metre from the closest part of the wall but possibly many metres from most of the wall surface. This means that even at a distance of one metre from the wall, the sound is already dispersed over a relatively large area, and the sound level at any position one metre from the wall is therefore lower than it would be if dispersed over the much smaller area 1m from a point source.

Therefore, the sound level close to a large source (in the near field) is lower than would be the case at the same distance from a small source. However, the corresponding reduction with increasing distance from the source is less than 6dB for every doubling of distance until the listener is far enough away from the source that it starts to act as a point source instead. At this distance the sound level becomes the same, regardless of the size of the source.