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# Inverse Square Law

## A doubling of the distance from a noise source will reduce the sound pressure level with 6 decibel

In a free field - a doubling of the distance from a noise source reduces the sound pressure level with 6 decibel.

This - the Inverse Square Law - can be expressed in a diagram like

dL = Lp2 - Lp1

= 10 log (R2 / R1)2

=  20 log (R2 / R1)                                        (1)

where

dL = difference in sound pressure level (dB)

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 - Rifle Shot and Sound Pressure at Distance

If the sound pressure from a rifle shot is measured to 134 dB at 1.25 feet - the reduction in sound pressure level at distance 80 feet can be calculated as

dL = 20 log ((80 ft) / (1.25 ft))

= 36 dB

The sound pressure level at distance 80 ft can be calculated as

Lp2 = (134 dB) - (36 dB)

= 98 dB

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

### Inverse Square Law Calculator

Use the calculator below to calculate the sound pressure level at distance.

Lp1 - sound pressure level at location 1 (dB)

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

Lp1 - distance from source to location 2 (m, ft)

### Example - Noise from a Machine

The noise from a machine in distance 1 m is measured to 110 dB. The noise reduction due to the inverse square law to a working area at distance 5 m can be calculated as

dL = 20 log ((5 m) / (1 m))

= 14 dB

The sound pressure level in the working area can be calculated as

Lp2 = (110 dB) - (14 dB)

= 96 dB

This noise level is only permitted for a limited amount of time and some action with partial barriers or enclosure of the machine should be done.

## Related Topics

• Acoustics - Room acoustics and acoustic properties - decibel A, B and C - Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation

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