Building Acoustics

124 Building acoustics

referred in section 4.5.1.1 above to the standard ISO 3741 on sound power determination
in a reverberation room, where a correction factor (1−α)was applied to the absorption
area (see Equation (4.32)). Vorländer (1995) has shown that this correction factor is an
approximation of the general term exp(A/S), where the absorption area is given by

A=− ⋅ − +Sln(1 α) 4mV. (4.43)

If m equals zero, we certainly arrive at the correction term in Equation (4.32) again as

ln(1 ) 4

0

ee 1

AS mV

SS

m

α

α.

−−−−+

=

⎡⎤

=⎢⎥

⎢⎥⎣⎦

=− (4.44)

Using this general correction, Vorländer (1995) obtains a very good fit, even up to 20
kHz, between the sound powers of a reference sound source determined in a
reverberation room as compared with a free field determination.

4.5.1.4 Sound field composing direct and diffuse field

When deriving Equation (4.28), we assumed that the sound field was an ideal diffuse
one; the energy density was everywhere the same in the room. It is obvious, however,
that the source must represent a discontinuity; even in a room having a very long
reverberation time there must exists a direct sound field in the neighbourhood of the
source. We shall have to distinguish between the source near field, where the sound
pressure may vary in a very complicated manner depending on the type of source, and
the far field where the sound pressure decreases regularly with the distance from the
source (see the discussion on sound sources in Chapter 3).
Assuming a position in the far field, we may apply the formula describing the
relationship between the source sound power and the pressure squared in an ideal
spherical (or plane) wave field:
2

00

d.

p

W

ρc

=∫ ⋅ S



v (4.45)

Initially, we shall assume that the source is a monopole, hence

(^2002)

1

.

4

pWc

r

ρ

π

 = (4.46)

For other types of source, we may introduce a directivity factor Dθ, thus write

2 00 2 ,

4

D

pWc

r

ρ θ

π

 = (4.47)

where r is the distance from the source. The index θ on the directivity indicates that the
latter generally depends on a properly defined angle. Combining this expression with the
simple one giving the pressure in a diffuse field, Equation (4.30), we arrive at the
following expression for the total sound field: