# Propagation of Sound Indoors

## Sound and noise in a room will 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 for a receiver can be expressed as:

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

where

L_{p}= received sound pressure level (dB)

L_{w}= sound power level from source (dB)

R= room constant (m^{2}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 (m^{2}Sabine)

A= absorption of the room (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

### 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/m^{2})

I_{i}= incident sound intensity (W/m^{2})

### Total Room Sound Absorption

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

A = S_{1}α_{1}+ S_{2}α_{2}+ .. + S_{n}α_{n}= Σ S_{i}α_{i}(4)

where

A= the absorption of the room (m^{2}Sabine)

S_{n}= area of the actual surface (m^{2})

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 (m^{2}Sabine)

S= total surface in the room (m^{2})

A rooms acoustic characteristics can be calculated with the formulas above, or estimated for typical rooms.

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