Propagation of Sound Indoors

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

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:

L_p = L_w + 10 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)

Room Constant

The room constant express an acoustic property of the room:

R = A / (1- α_m)

= Σ S_i α_i / (1- α_m) (2)

where

R = room constant (m² Sabin)

A = absorption of the room (m² Sabin)

α_m = mean absorption coefficient of the room

S_i = individual surface area in the room (m²)

α_i = absorption coefficient for individual surface in the room

Absorption Coefficient

The sound absorption coefficient indicates how much of the sound is absorbed in the actual material. The absorption coefficient can be expressed as:

α = I_a / I_i (3)

where

I_a = sound intensity absorbed (W/m²)

I_i = incident sound intensity (W/m²)

Total Room Sound Absorption

The total sound absorption in a room can be expressed as:

A = S₁ α₁ + S₂ α₂ + .. + S_n α_n = Σ S_i α_i (4)

where

A = the absorption of the room (m² sabine)

S_n = area of the actual surface (m²)

α_n = absorption coefficient of the actual surface

Mean Absorption Coefficient

The mean absorption coefficient for the room can be expressed as:

a_m = A / S (5)

where

a_m = 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.

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