Directivity Coefficient and Sound Attenuation 

The attenuation in a room depends on the receiver and source location. 

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 sabin)

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, the attenuation - L_p - L_w - can be estimated from the diagram below:  

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