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Sound - Attenuation and the Directivity Coefficient

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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

(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

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.

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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