Abatement and Distance from Source

The disruption of sound pressures waves which reduces the noise is called attenuation - Sound Pressure Level Calculator

Spherical Distance

sound pressure in distance from source

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

sound pressure in distance from source

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 more generic expression can be formulated to:

p² = D ρ c N / (4 π r²) (3)

where

D = directivity coefficient (1 spherical, 2 half sperical)

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 logarithmic 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

L_p = sound pressure level (dB)

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