Sound absorbers 183
above is that Wilson’s model also repairs the anomaly of the Delany-Bazley model
giving a realistic prediction over a far broader frequency range. In fact, predictions at low
frequencies coincide very well with the ones by Mechel’s model rendering it unnecessary
to “splice” models in order to cover a broader frequency range. The latter comparison is
not given by Wilson but is easily demonstrated.
5.5.3 Absorption as a function of material parameters and dimensions
It is interesting and of great practical importance as well, to know the way in which
material parameters and dimensions do influence the absorption capabilities of a porous
material. The influence of the parameters is easy to show in models involving just one or
may be two parameters. For models having a great number of parameters, as the ones
given below, it is rather difficult to give a complete overview. We shall therefore restrict
the following illustrations, to the effect of varying the flow resistivity and thickness of
the sample, to the model of Delany and Bazley. Furthermore, to make the illustrations
simple, most data shown in this chapter apply to normal sound incidence on the actual
absorbing surface. Referring back to the treatment in Chapter 3, on absorption by oblique
and ultimately diffuse sound incidence, it will be appropriate also to illustrate this effect.
A further presumption to these calculations is that the actual surface is “infinitely”
large. In practice, this implies that the surface is sufficiently large in comparison to
wavelength thus enabling us to neglect any effects due to the outer free edges. On finite
size samples there will, however, always be some diffraction effects along the edges, the
so-called edge effect. The result is an increase in the effective absorption area, which
means that the “acoustic area” is larger than the geometrical area. One may therefore end
up with data for the absorption factor larger than one (1.0) when dividing the measured
total absorption area by the area of the absorber.
As mentioned when presenting the measurement methods for absorption, this effect
still shows up in results from reverberation room measurements in spite of the rather
large area specified (10–12 m^2 ) and a ratio of width to length between 0.7 and 1.0 just to
minimize this effect. Thomasson (1980), using the sound field distribution above a finite
absorbing surface surrounded by a hard surface, which corresponds to a reverberation
room situation, calculated the effective statistical absorption factor as a function of area.
We shall illustrate the importance of absorber size by using Thomason’s expression to
compare with measured data from a reverberation room test.
5.5.3.1 Flow resistivity and thickness of sample
In the introduction it was mentioned that the normal mounting of a porous absorber is
either directly on to a hard surface or at a certain distance from it, i.e. leaving a cavity
behind it. For ceilings, the latter is the normal mounting, not only because there must be
some space for the service equipment but one gains additional absorption at the lower
frequencies. We will start giving some results where the absorber is directly attached to a
hard and infinitely large surface.
A typical result when varying the thickness of porous absorber is shown in Figure
5.20. The absorption factor is calculated for normal incidence and for thickness in the
range of 25 to 100 mm, the flow resistivity being 10 kPa⋅s/m^2. As is apparent from the
figure, the thickness has to be large to obtain high absorption at the lower frequencies.
The physical explanation is that waves having the larger wavelengths penetrate far into
the material, also being less attenuated and thereby reflected from the back wall.