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Sound Propagation - the Inverse Square Law

Doubling of the distance from a noise source reduces the sound pressure level with 6 decibel.

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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

sound pressure level vs. distance from source - inverse square law

Download and print the Inverse Square Law chart - Sound pressure level reduction vs. distance from source

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

Sound Propagation - the Inverse Square Law
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.

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.

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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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