Directivity Coefficient and Sound Attenuation 

The attenuation in a room depends on the location of the source and the receiver, and the room constant

For a continuing sound source, the sound level in a room is the sum of direct and reverberant sound. The sound pressure for a receiver can be expressed as:

L_p = L_w + log( D / ( 4 π r² ) + 4 / R)          (1)

where

L_p = received sound pressure level (dB)

L_w = sound power level from source (dB)

D = directivity coefficient

R = room constant (m² Sabine)

π = 3.14

r = distance from source (m)

The figure below can be used to approximate the Directivity coefficient - D - for typical locations of the receiver and the sound source:

(1) can be transformed to express the difference between the received sound pressure and emitted sound power - the attenuation - as: 

L_p - L_w =  10 log( D / ( 4 π r² ) + 4 / R)          (2)

Combining (2) with the ratio between distance - r - from source and square of the directivity coefficient - D, and the rooms absorption - m² Sabine.

Sound Attenuation Calculator

D - directivity coefficient

R - room constant - (m² Sabine)

r - distance from source (m)

Sound Attenuation - (L_p - L_w) - (dB) :

The attenuation - (L_p - L_w) - can also be estimated from the diagram below:  

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