Sound Propagation - the Inverse Square Law
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.
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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