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
dL = L_{p2}  L_{p1}
= 10 log (R_{2} / R_{1})^{2}
= 20 log (R_{2} / R_{1}) (1)
where
dL = difference in sound pressure level (dB)
L_{p1} = sound pressure level at location 1 (dB)
L_{p2} = sound pressure level at location 2 (dB)
R_{1} = distance from source to location 1 (ft, m)
R_{2} = 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
L_{p2} = (134 dB)  (36 dB)
= 98 dB
Distance (feet)  Sound Pressure L_{p} (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.
L_{p1}  sound pressure level at location 1 (dB)
R_{1}  distance from source to location 1 (m, ft)
R_{2}  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
L_{p2} = (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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