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Engineering ToolBox > Propagation of Sound Indoors
For a continuing sound source in a room, the sound level is the sum of direct and reverberant sound. The sound pressure for a receiver can be expressed as:
Lp = Lw + 10 log( D / ( 4 π r2 ) + 4 / R) (1)
where
Lp = received sound pressure level (dB)
Lw= sound power level from source (dB)
R = room constant (m2 Sabin)
π = 3.14
r = distance from source (m)
The room constant express an acoustic property of the room:
R = A / (1- αm)
= Σ Si αi / (1- αm) (2)
where
R = room constant (m2 Sabin)
A = absorption of the room (m2 Sabin)
αm = mean absorption coefficient of the room
Si = individual surface area in the room (m2)
αi = absorption coefficient for individual surface in the room
The sound absorption coefficient indicates how much of the sound is absorbed in the actual material. The absorption coefficient can be expressed as:
α = Ia / Ii (3)
where
Ia = sound intensity absorbed (W/m2)
Ii = incident sound intensity (W/m2)
The total sound absorption in a room can be expressed as:
A = S1 α1 + S2 α2 + .. + Sn αn = Σ Si αi (4)
where
A = the absorption of the room (m2 sabine)
Sn = area of the actual surface (m2)
αn = absorption coefficient of the actual surface
The mean absorption coefficient for the room can be expressed as:
am = A / S (5)
where
am = mean absorption coefficient
A = the absorption of the room (m2 sabine)
S = total surface in the room (m2)
A rooms acoustic characteristics can be calculated with the formulas above, or estimated for typical rooms.