Propagation of Sound Indoors

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

Sound Propagation 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)


Lp = received sound pressure level (dB)

Lw= 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- αm)

    = Σ Si αi / (1- αm)         (2)


R = room constant (m2 Sabine)

A = absorption of the room (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

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 = Ia / Ii         (3)


Ia = sound intensity absorbed (W/m2)

Ii = 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 + .. + Sn αn = Σ Si αi         (4)


A = the absorption of the room (m2 Sabine)

Sn = area of the actual surface (m2)

αn = absorption coefficient of the actual surface

Mean Absorption Coefficient

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

am = A / S         (5)


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.

Related Topics

  • Acoustics - Room acoustics and acoustic properties - decibel A, B and C - Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation
  • Noise and Attenuation - Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems

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