Equivalent sound absorption

The equivalent sound absorption area A in m² is the area representing a room’s entire sound absorption (walls, ceiling, decoration etc. – sound absorption coefficient 100%). It is the sum of the products of all limiting partial surfaces S_i (including the surfaces of objects within the room) and their sound absorption coefficients α_i. The larger a room’s equivalent absorption area, the more muted and the quieter it is.

The equation for the equivalent sound absorption area A is illustrated in figure. It allows for the determination of A in relation to room volume V and reverberation time T.

The difference

between sound power level LWA and sound pressure level LPA is depicted in relation to the equivalent sound absorption area A in figure 5.62b. It facilitates the determination of the sound pressure level present in a given room based on measured sound power levels as contained e.g. in the design documents for ventilated luminaires.

With multiple sound sources (number N) of identical sound power level L_WA, the overall sound power level L_{WA, total} is increased by ΔL₂ according to the formula

This formula is analysed in figure c.

Example
For an office room with a room volume V = 200 m³ and a reverberation time T = 0.5 s – see table – the resulting equivalent sound absorption area A = 65 m², figure a.
Hence, the difference between sound power level L_WA and sound pressure level L_PA is 12 dB(A); figure b. For a sound source (e.g. a ventilated luminaire) with a sound power level L_WA = 30 dB(A) in this room, the expected sound pressure level L_PA = 30 dB(A) - 12 dB(A) = 18 dB(A). If the room contains e.g. 12 sound sources of identical loudness, the overall sound power level rises from 30 dB(A) to ca. 41 dB(A) according to figure c.