Building Acoustics

Sound absorbers 187

where Re again denote the real part of the actual quantity.
In Figure 5.23, we have again used a porous material with a thickness of 50 mm as
an example. The angle of incidence is varied between zero and 89 degrees, i.e. between
normal incidence and nearly grazing incidence. One can observe the larger absorption
obtained for oblique incidence, however approaching zero by grazing incidence. The
dotted curve shows the statistical absorption factor calculated from Equation (5.57).

100 1000

200 400 600 800 2000 4000

Frequency (Hz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

A

bso

rption facto

r

Normal incidence

Diffuse - infinite

Diffuse - 3.6 m

Measured - 3.6 m

Diffuse - 1.2 m

Measured - 1.2 m

Figure 5.24 Statistical absorption factor of a porous absorber having different areas, 50 mm mineral wool (r =
30 kPa⋅s/m^2 ) with hard backing. The test area is square with dimensions indicated. The corresponding predicted
absorption factors for an infinitely large specimen, both for normal and diffuse sound incidence, are also shown.
Prediction method for finite size specimen and corresponding measurement data (reverberation room) from
Thomasson (1982).

It now remains to see how the last result would turn out if one cannot assume that
the lateral dimensions of the sample are not very large compared to the wavelength. We
have indeed up to now assumed that the area of the absorber was infinitely large. That
we must take account of a finite size absorber does not only apply in a standard
reverberation room measurement, but certainly in normal practical applications.
Thomasson (1980) has shown, again assuming that the absorber is locally reacting, that
we should substitute Equation (5.57) by

{}

/2 2

n

stat 2

00 nf

4Re sin

dd,

Z

ZZ

ππ

φ

αφθ

π

=

+

∫∫ (5.58)