Sound absorbers - Building Acoustics - page 188

where Z f is denoted field impedance , a quantity that may be interpreted as a radiation
impedance for a plane surface having the same shape as the absorber and the same
velocity distribution. Thus, Z f will be a function of the shape and dimensions of the
specimen as well as a function of the frequency and the angle of incidence. It should be
noted that the direction of incidence must be specified both by the angle ϕ with the
surface normal as well as the azimuth angle θ.
One may interpret this in another way by using an electrical analogue, a circuit
where Z f ⋅ Z 0 is the internal impedance of a generator twice the sound pressure in the
incoming wave and where Z n ⋅ Z 0 is the outer load impedance. The expressions giving Z f
are quite complicated integrals that normally have to be solved numerically. As expected,
Equation (5.58) is approaching Equation (5.57) when the linear dimensions of the
absorber get large compared to the wavelength because then Z f ≈ 1/cosϕ.
Figure 5.24 shows predicted results compared with measurements data from a
reverberation room test. According to Thomasson (1982), the test sample is mineral wool
of 50 mm thickness having a flow resistivity of 30 kPa⋅s/m 2 . His measurement data from
the reverberation room tests are given in one-third-octave bands. Measurements and
predictions are performed on three different sample areas of which we show the results
for the two areas, 1.2 x 1.2 m 2 and 3.6 x 3.6 m 2 .
For the calculated results in Figure 5.24 we have again used the model by
Delany and Bazley to describe the mineral wool. For comparison, we have also given the
result for the absorption factor at normal sound incidence as well as for diffuse sound
incidence using Equation (5.57) , i.e. data corresponding to the ones shown in Figure
5.23. As is evident from Figure 5.24, the increase in the statistical absorption factor for a
finite sample size is quite dramatic, even for the sample having a side length 3.6 of
metres; which in fact is a common size for reverberation room tests. As we also may
observe the fit between measured and calculated results is generally very good. It should
be mentioned that Thomasson's calculated values for one-third-octave bands are not
shown in the figure. This is because the differences between his calculated results and
the ones plotted are negligible.
We shall round off this discussion of the edge effect by presenting an
illustration showing how it can be utilized in practice. As an alternative to attaching a
certain amount of absorbers on to a wall or ceiling covering one single area one may, if
this is not unsuitable, split the absorber into smaller patches separated by some distance.
Figure 5.25 shows results from an experiment conducted in a reverberation room. Eight
blankets of 25 mm thick mineral wool, each having a dimension of 0.6 times 1.2 metres,
was first arranged as one single area and thereafter separated as shown in the sketch
beside the figure. As the total area when placed adjacent to one another (5.8 m 2 ) is less
the 10 m 2 required for a normal test, the edge effect for the lowest curve will be larger
than normal. However, when pushing the blankets away from each other the increase in
the absorption is very large. (It should be noted that the absorption factor is calculated for
an area of 5.8 m 2 in all cases).
Holmberg et al. (2003) have developed a prediction model to calculate the
statistical absorption factor of such absorbing patches arranged in a periodic pattern. The
measurement data shown above were, in fact, used to compare with their predictions.
The predicted results, which compared favorably with the measured ones, are, however,
not shown here.