Building Acoustics

Sound absorbers 191

to calculate Zc and Γ according to Equations (5.60) and (5.61), which in turn enable us to
calculate the results shown in Figure 5.26 using a general calculation routine based on
transfer matrices (see section 5.7.1 and Equation (5.85)).
Certainly, in this case more simple models could probably have been used as the
pores in the wooden material are straight tubes directed normally to the surface of the cut
discs.

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

A

bsorption

factor

d = 10 mm

l = 40 mm

d = 5 mm

l = 85 mm

Figure 5.26 Normal incidence absorption factor of a disc of porous wood (rattan palm) mounted in front of a
hard wall. Disc thickness (d) and cavity depth (l) is indicated. Solid curves – measured. Dashed curves –
predicted. See also description in the text.

5.5.4.2 The model of Allard/Johnson

This model (see e.g. Allard (1993)) exchanges the non-measurable quantity sf in the
Attenborough formulation with two other parameters. These are the characteristic viscous
length Λ and the characteristic thermal length Λ', which are defined in the following way

2

iw

2

i

()d

2

and.

()d

S

V

vr S

2 A

vr V V

=

ΛΛ′

∫

∫

v

= (5.64)

In the expression for Λ the numerator is a surface integral where the velocity vi of the
fluid, as indicated by the index w, applies to the inner walls of the pores. The
denominator is the corresponding volume integral that applies to the whole volume of
pores. The thermal length Λ' is given by the ratio of the total inner surface area A to the
total volume V of the pores.
The great advantage in using this description is that it is possible to determine both
parameters separately by ultrasonic measurement technique (see below for measurements