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Engineering ToolBox > Abatement and Distance from Source

The disruption of sound pressures waves which reduces the noise is called attenuation

Spherical Distance

The sound pressure in a spherical distance from a source can be expressed as:

p² = ρ c N / (4 π r²) (1)

where

p = sound pressure (Pa, N/m²)

ρ = density of air (kg/m³)

c = speed of sound (m/s)

N = sound power (W)

π = 3.14

r = distance from source (m)

Half Spherical Distance

The sound pressure in a half spherical distance from a source can be expressed as:

p² = ρ c N / (4 π r² / 2) = 2 ρ c N / (4 π r²) (2)

A generic expression can be formulated as:

p² = D ρ c N / (4 π r²) (3)

where

D = directivity coefficient

The directivity coefficient depends on several parameters - the position and direction of the source, the room or the surrounding area, etc.

The Sound Pressure Level - L_p - can be expressed as:

L_p = 20 log ( p / p_ref ) = 20 log ( (D ρ c N / (4 π r²))^1/2 / p_ref )

= 20 log ( 1/r (D ρ c N / (4 π))^1/2 / p_ref ) (4)

where

p_ref = 2 10^-5 - reference sound pressure (Pa)

Note! For every doubling of the distance from the noise source, the sound pressure levels - L_p, will be reduced by 6 decibels.