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Propagation of Sound Indoors - Room Constant

Sound and noise in a room reach the receiver as direct and reverberant sound

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

Lp = LN + 10 log (D / (4 π r2) + 4 / R)                                 (1)

where

Lp = received sound pressure level (dB)

LN = sound power level from source (dB)

D = directivity coefficient (typical 1 for receivers in the middle of the room)

R = room constant (m2 Sabin)

π = 3.14....

r = distance from source (m)

Room Constant

The room constant express the acoustic property of a room.

R = A / (1- αm)

    = Σ Si αi / (1- αm)                                    (2)

where

R = room constant (m2 Sabine)

A = total room sound absorption (m2 Sabine)

αm = mean absorption coefficient of the room

Si = individual surface area in the room (m2)

αi = absorption coefficient for individual surface in the room

Example - Received Sound

The sound power generated from a machine is 90 dB. The machine is located in a room with total sound aborption 12.2 m2 Sabine and mean absorption coefficient 0.2.

The room constant can be calculated as

R = (12.2 m2) / (1 - 0.2)

   = 15.3 m2 Sabine

For a receiver located in the middle of the room with a directivity coefficient 1 and distance 2 m from the source - the received sound pressure level can calculated as

Lp = (90 dB) + 10 log (1 / (4 π (2 m)2) + 4 / (15.3 m2 Sabine)) 

     = 84.8 dB

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