Abatement and Distance from Source

The disruption of sound pressure waves reducing the noise is called attenuation - Sound Pressure Level Calculator

Spherical Distance


sound pressure in distance from source

Sound pressure in spherical distance from a noise source can be calculated as:

p2 = ρ c N / (4 π r2)         (1)


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

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)


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

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 - Lp - can be expressed logarithmic as:

Lp = 20 log( p / pref ) = 20 log ((D ρ c N / (4 π r2))1/2 / pref )

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


Lp = sound pressure level (dB)

pref = 2 10-5 - reference sound pressure (Pa)

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

Sound Pressure Level Calculator

ρ - air density (kg/m3)

c - sound velocity (m/s)

N - sound power (W)

r - distance from source (m)

D - directivity coefficient

Sound Pressure Level (dB) :  

Example - Sound Pressure from Wood Planer

If the sound power generated from a wood planer can be estimated to 0.01 W - the sound pressure in a distance 10 m from the tool can be calculated as

Lp = 20 log ((D ρ c N / (4 π r2))1/2 / pref )

   = 20 log(2 (1 kg/m3) (331.2 m/s) (0.01 W) / (4 π (10 m)2))1/2 / (2 10-5 Pa))

   = 71 dB      

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

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