Building Acoustics

Sound absorbers 201

sair

air

air

sHe

He

He (^0) i
and
where i.
k b L k b L
υ
π
υ μ
υ
πρ

=

⎛⎞

==⎜⎟

⎝⎠

(5.74)

How this linear approximation based on Equation (5.71) looks like compared with
calculated results using the complete model is shown in Figure 5.35. By the notion
complete model we understand the one where the complex wave number k ́ is calculated
from Equations (5.65) and (5.66). The suitability of the linear approximation is certainly
dependent on the ratio of Λ to Λ′, which in the example is 1:2. By using a frequency
range upwards from 250 kHz, the method seems to be accurate within 10–15 %. More
information may be found in the referenced paper.

5.7 Prediction methods for impedance and absorption

Both commercial and specially made sound absorbers are rarely a simple and
homogeneous structure. As an example, a fabric of some kind, a plastic membrane, a
perforated panel etc., may cover a porous material. The whole structure may then be
mounted at a certain distance from a wall or ceiling. We have given several examples of
data for such absorbers in the sections above. Here we shall give a short review of the
prediction method used.
A number of the elements or layers making up the structure of a given absorber
may not be characterized as being locally reacting. This implies, not only that the input
impedance will depend on the angle of sound incidence, but we will also get a lateral
wave movement, i.e. along the actual surface. We then have to take the dimensions and
the boundary conditions into account. We may accomplish this by applying models using
finite element methods (FEM). There is software, also commercially available, to
perform acoustic calculations on absorbers, especially on porous materials. We gave an
example earlier (see also Figure 5.30).

pi

pr pt

φ

φ

Figure 5.36 A construction composed of several layers, each of infinite extent.