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Sound - Attenuation and the Directivity Coefficient

The attenuation in a room depends on the location of the sound source and the receiver - and the room constant.

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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

Lp = LN + log (D / (4 π r2) + 4 / R)                                                          (1)


Lp = received sound pressure level (dB)

LN = sound power level from source (dB)

D = directivity coefficient

R = room constant (m2 Sabine)

π = 3.14 .....

r = distance from source (m)

Directivity coefficient - D

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

sound directivity coefficient

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

Lp - LN =  10 log (D / (4 π r2) + 4 / R)                                                                 (2)

Room Sound Attenuation Calculator

D - directivity coefficient

R - room constant - (m2 Sabine)

r - distance from source (m)

Room Sound Attenuation (Lp - LN) - (dB) :

The attenuation (Lp - LN) can also be estimated from the diagram below by modifying (2) to be expressed as the ratio between "distance r between source and receiver" and "square of the directivity coefficient D" - and the total room sound absorption in m2 Sabine.

Sound attenuation - directivity coefficient - sabin

Example - Sound Attenuation in a Room 

For a room the acoustic property total room sound absorption is 1000 m2 Sabine.  For a listener in the middle of the room with a directivity constant 1 and at distance 1 m from the sound source - the ratio

r / D1/2 = 1 / (1 m)1/2

          = 1

From the diagram above the attenuation can estimated to approximately

10 dB

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  • Engineering ToolBox, (2003). Sound - Attenuation and the Directivity Coefficient. [online] Available at: [Accessed Day Mo. Year].

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