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Propagation of Sound Indoors - the Room Constant

In a room the sound or noise 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 level for a receiver can be expressed as:

L p = L N + 10 log (D / (4 π r 2) + 4 / R)                                  (1)


L p = received sound pressure level (dB)

L N = sound power level from source (dB)

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

R = room constant (m 2 Sabin)

π = 3.14 ....

r = distance from source (m)

Room Constant

The room constant express the acoustic property of a room.

R = A / (1- α m)

    = Σ S i α i / (1- α m)                                     (2)


R = room constant (m 2 Sabine)

A = total room sound absorption (m 2 Sabine)

α m = mean absorption coefficient of the room

S i = individual surface area in the room (m 2)

α i = 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 m 2 Sabine and mean absorption coefficient 0.2.

The room constant can be calculated as

R = (12.2 m 2) / (1 - 0.2)

   = 15.3 m 2 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

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

     = 84.8 dB

Related Topics

  • Acoustics

    Room acoustics and acoustic properties. decibel A, B and C calculations. Noise Rating (NR) curves. Sound transmission through walls. Calculate 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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