# 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:

L_{p}= L_{N}+ 10 log (D / (4 π r^{2}) + 4 / R)(1)

where

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)

where

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*

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