acoustics

Inverse-Square Law

Acoustics / Noise

The law by which the mean-square Sound Pressure Level varies inversely as the square of the distance from the source. The general rule of thumb is that, under ideal conditions (no reflecting surfaces or other background sound or interference), a sound level drops 6 dB for every doubling of the distance from the source. If the two distances in question are d1 and d2, then the decibel difference ΔD is:

ΔD = 10 log (d1/d2)2 = 20 log (d1/d2)

The table below can be used to find the correction for distance such as in the case of distances quoted in noise measurement specifications, assuming ideal conditions. Take the given distance on the left-hand column and find the correction in the vertical column under the distance for which the correction is desired. Add the correction to the given level to find the corrected level.

For a discussion of environmental effects, see sound propagation. Note that this table applies only to point sources and free field conditions. See: Simple Sound Source.

Corrected Distance (ft)

Given Distance (ft)
 3
 5
 10
 15
 20
 25
 30
 40
 50
 60
 70
 80
 90
 100
3
 0
 - 4.4
 -10.5
 -14.0
 -16.5
 -18.0
 -20.0
 -22.5
 -24.4
 -26.0
 -27.4
 -28.5
 -29.5
 -30.5
5
 4.4
 0
 - 6.0
 - 9.5
 -12.0
 -14.0
 -15.6
 -18.1
 -20.0
 -21.6
 -22.9
 -24.1
 -25.1
 -26.0
10
 10.5
 6.0
 0
 - 3.5
 - 6.0
 - 8.0
 - 9.5
 -12.0
 -14.0
 -15.6
 -16.9
 -18.1
 -19.1
 -20.0
15
 14.0
 9.5
 3.5
 0
 - 2.5
 - 4.4
 - 6.0
 - 8.5
 -10.5
 -12.0
 -13.4
 -14.5
 -15.6
 -16.5
20
 16.5
 12.0
 6.0
 2.5
 0
 - 1.9
 - 3.5
 - 6.0
 - 8.0
 - 9.5
 -10.9
 -12.0
 -13.1
 -14.0
25
 18.0
 14.0
 8.0
 4.4
 1.9
 0
 - 1.6
 - 4.1
 - 6.0
 - 7.6
 - 8.9
 -10.1
 -11.1
 -12.0
30
 20.0
 15.6
 9.5
 6.0
 3.5
 1.6
 0
 - 2.5
 - 4.4
 - 6.0
 - 7.4
 - 8.5
 - 9.5
 -10.5
40
 22.5
 18.1
 12.0
 8.5
 6.0
 4.1
 2.5
 0
 - 1.9
 - 3.5
 - 4.9
 - 6.0
 - 7.0
 - 8.0
50
 24.4
 20.0
 14.0
 10.5
 8.0
 6.0
 4.4
 1.9
 0
 - 1.6
 - 2.9
 - 4.1
 - 5.1
 - 6.0
60
 26.0
 21.6
 15.6
 12.0
 9.5
 7.6
 6.0
 3.5
 1.6
 0
 - 1.3
 - 2.5
 - 3.5
 - 4.4
70
 27.4
 22.9
 16.9
 13.4
 10.9
 8.9
 7.4
 4.9
 2.9
 1.3
 0
 - 1.2
 - 2.2
 - 3.1
80
 28.5
 24.1
 18.1
 14.5
 12.0
 10.1
 8.5
 6.0
 4.1
 2.5
 1.2
 0
 - 1.0
 - 1.9
90
 29.5
 25.1
 19.1
 15.6
 13.1
 11.1
 9.5
 7.0
 5.1
 3.5
 2.2
 1.0
 0
 - 0.9
100
 30.5
 26.0
 20.0
 16.5
 14.0
 12.0
 10.5
 8.0
 6.0
 4.4
 3.1
 1.9
 0.9
 0

Decibel corrections for variations in distance from source. An example: a sound source of 60 dB is measured at 50 feet; if the measurement were at 15 feet, the level would be 60 + 10.5 = 70.5 dB under ideal conditions.