Inverse Square Law

For every doubling of the distance from the noise source, the sound pressure levels - Lp, will be reduced by 6 decibels

For a free field every doubling of the distance from the noise source, the sound pressure levels - Lp, will be reduced by 6 decibels. The inverse square law can be expressed as in the diagram below.

sound pressure inverse square law

Lp2 - Lp1 = 10 log (R2 / R1)2

            =  20 log (R2 / R1)

where

Lp1 = sound pressure level at location 1 (dB)

Lp2 = sound pressure level at location 2 (dB)

R1 = distance from source to location 1 (ft, m)

R2 = distance from source to location 2 (ft, m)

A "free field" is defined as a flat surface without obstructions.

Example - Shot of a Rifle and Decibel Level

Distance
(feet)
Sound Pressure
Lp
(decibel)
1.25 134
2.5 128
5 122
10 116
20 110
40 104
80 98
160 92
320 86
640 78
1280 74
2560 68
5120 62

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