10.1Sound Power, Acoustic Intensity, and Energy Density

w ¼ PRMSVRMSS

And the units in the MKS system are:

whJs i ¼ PhmN2i V hms i S m2

For plane waves moving at the speed of sound c, because VRMS ¼ PRMS, the sound

ρoc

power is:

P2

w ¼ RMS S ðplane wavesÞ

ρoc

Remarks

The sound power of an acoustic source is the energy of an enclosed surface of the acoustic source.

10.1.2 Definition of Acoustic Intensity

The acoustic intensity I is defined as the energy per unit time per unit area or (by the definition of sound power) the sound power w per unit area S as:

I wS

Based on the definition of sound power w, acoustic intensity I can be formulated in terms of the RMS pressure PRMS and the RMS velocity VRMS as:

I ¼ w ¼ PRMSVRMSS ¼ PRMSVRMS

S S

And the units in the MKS system are:

For plane waves moving at the speed of sound c, because VRMS ¼ PRMS as shown

ρoc

in Chap. 4, the acoustic intensity is:

P2

I ¼ RMS ðplane wavesÞ

ρoc

10.1.3 Definition of Energy Density

The energy density δ is defined as the energy per unit volume and can be formulated in terms of sound power w (energy per unit time) as:

δ cSw

Based on the definition of sound power w, energy density δ can be formulated in terms of the RMS pressure PRMS and the RMS velocity VRMS as:

And the units in the MKS system are:

For plane waves moving at the speed of sound c, because VRMS ¼ PRMS as shown

ρoc

in Chap. 4, the acoustic intensity is:

P2

δ ¼ RMS ðplane wavesÞ

ρoc2

Note that the acoustic intensity is useful for deriving formulas for room acoustics because it is defined as the energy per unit volume and can be formulated based on the conservation of energy.

10.2Absorption Coefficients, Room Constant, and Reverberation Time

10.2.1 Absorption Coefficient of Surface

The statistical absorption coefficient or random incidence sound absorption coeffi- cient, α, is frequency-dependent and is defined as the ratio of acoustic energy absorbed by a surface to the acoustical energy incident upon the surface when the

incident sound field is perfectly diffused, α wi wr .

wi

The absorption coefficient of a material is a number between 0 and 1 that indicates the proportion of sound which is absorbed by the surface compared to the incident sound. A large, fully open window would offer no reflection, as any sound reaching it would pass straight out and no sound would be reflected. This would have an

absorption coefficient of 1. Conversely, a thick, smooth painted concrete ceiling would be the acoustic equivalent of a mirror and have an absorption coefficient very close to 0.

Sound absorption coefficients of common materials used in buildings are presented in the table below.

Table: Absorption coefficients of general building materials

Since different surfaces of a room will, in general, have different absorption coefficients, an average sound absorption coefficient α need be calculated for a given room:

n

P Siαi α ¼ i¼1n

P

Si

i¼1

where:

Si¼ area of the i-th surface.

αi¼ absorption coefficient at the i-th surface.

Excess Absorption Coefficient Due to Air

For large rooms and frequencies above 2000 Hz, air absorption (not including surface absorption) may become significant. The absorption due to air in the room is represented by the excess absorption coefficient and is given by:

k¼ experimentally determined coefficient of air (see table below) D ¼ 4SV (distance between ceiling and floor)

V¼ volume of the room S¼ total surface area

where D is the average traveling distance between ceiling and floor. The formula D is based on a half cube of 10 [m] by 10 [m] by 5 [m] as shown below:

4 × 5 × 10 × 10

2 × 10 × 10 + 4 × 5 × 10

=

where

The total average absorption coefficient then becomes:

α0 ¼ αtot ¼ α þ αex

Approximate values for the coefficient k in metric units [3]