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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.

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

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

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)

R2 - 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.

## Related Documents

• ### Logarithms

The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.
• ### Noise - EPA Protective Levels

The noise level should not exceed certain values to protect public health and welfare.
• ### Noise from Machines - Enclosures and Sound Pressure Level Reductions

Barriers and enclosures to reduce noise sound pressure levels from machines.
• ### Optical Distance Law

Geometric dilution of light vs. distance.
• ### Required Voice Level at Distance

Distance and perception of voice.
• ### Sound - Abatement vs. the Distance from Source

The disruption of the sound pressure wave and the reduction of noise is called attenuation - Sound Pressure Level vs. distance calculator.
• ### Sound Pressure

Sound Pressure is the force of sound on a surface perpendicular to the propagation of sound.

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## Citation

• The Engineering ToolBox (2005). Sound Propagation - the Inverse Square Law. [online] Available at: https://www.engineeringtoolbox.com/inverse-square-law-d_890.html [Accessed Day Month Year].

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9.19.12