172 Building acoustics
situation, which was mentioned in section 5.2.3, are when using the so-called micro-
perforated panels, panels where the perforations with holes or slits have a typical linear
dimension less than 0.5 mm.
bldS 0Sa) b)
Figure 5.11 Distributed Helmholtz resonators. a) panel perforated by holes and backed by a cavity. b) slatted
panel backed by a cavity.
It was also pointed out that one normally adjusted the resistance by filling, partly or
wholly, the void behind the panel with a porous material, commonly mineral wool, or by
gluing a thin fabric on to the backside of the panel. This was shown in Figure 5.2. There
are several points to be noted concerning these solutions. The simple model used above
is not valid when filling the void, wholly or partly, by a porous material. The model
presupposes an empty air space and filling it modifies the resonance frequency calculated
using Equation (5.39). The actual frequency will normally be lower. Furthermore, the
particle velocity in the openings will be inversely proportional to the rate of perforation.
We must take account of this when adjusting the resistance of the system. Using for
example a porous material with a flow resistivity r and if we shall need a total flow
resistance of R (Pa⋅s/m), this means that the thickness of the material required is R⋅ε /r.
Figure 5.12 shows an example of calculated absorption factors at normal incidence
for a distributed resonator of the type shown in Figure 5.11 a). The plate (panel) has a
thickness of 1 mm and placed against a cavity having a depth of 100 mm. The plate is
perforated with holes having a diameter of 3 mm and the area allotted to each hole is 100
mm^2 , i.e. the perforation rate is approximately 7%. The lowest curve gives the result
without any porous layer or fabric at the back of the plate, with the others a porous layer
is added having the indicated total resistance. The calculations do not presuppose that the
depth of the cavity is less than the wavelength. This means that, in addition to the broad
peak around the resonance frequency according to Equation (5.39), we will see the effect
of the standing waves in the cavity at higher frequencies.
A further example is given in Figure 5.13, showing measured results from a
standard reverberation room test on a distributed resonator of the type discussed above.
The panels, placed against a cavity of depth 50 mm, are measured having only a fabric of
flow resistance 190 Pa·s/m glued to them as well as combined with the cavity filled with
a high density porous material, rock wool 70 kg/m^3.
Furthermore, the rather thick panel of 14 mm allows the holes, normally cylindrical
of diameter 8 mm, to have a conical shape (see insert to the figure), which may greatly
enhance the absorption of this type of resonator absorbers (see Vigran (2004)). As seen
from the results, filling the cavity completely with a porous absorber improves the low
frequency absorption. However, by changing the shape of the perforations only, an
amazing added improvement is attained.