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Engineering ToolBox > Propagation of Sound Outdoors

Outdoor propagation of sound - distance and attenuation. 

Single Sound Source - Spherical Propagation

The sound energy in the propagation direction of the sound is inversely proportional to the increasing surface area the sound  propagates through. The sound pressure level in a spherical distance - r - from a single sound source can be expressed as: 

L_p = L_w - 10 log( 4 Π r²)       (1)

where

L_p = sound pressure level (dB)

L_w = sound power level source in decibel (dB)

r = distance from source   (m)

(1) can also be expressed as: 

L_p = L_w - 20 log( r) + K'      (1b)

where 

K' = -11 (single sound source  and spherical distance) 

Single Sound Source - Hemi Spherical Propagation

When the sound source propagates hemi spherically with the source near ground, the constant can be set to 

• K' = - 8

Note! When the distance - r - from a power source doubles, the sound pressure level decreases with 6 dB. This relationship is also known as the inverse square law.

Other factors affecting the radiation of the sound are the direction of the source, barriers between the source and the receiver, and atmospheric conditions. Equation (1) can be modified to: 

L_p = L_w - 20 log r + K' + DI - A_a - A_b      (2)

where

DI = directivity index

A_a = attenuation due to atmospheric conditions

A_b = attenuation due to barriers

Linear Sound Source

With a linear sound source, like a road or high way with heavy traffic, the sound pressure can be expressed as:

L_p = L_w - 10 log( 4 Π r)       (3)

Note! When the distance - r - from a linear power source doubles, the sound pressure level decreases with 3 dB.