Building Acoustics

Room acoustics 141

optics may be used. We shall not treat any of these methods here, but to illustrate the
effect of these diffusers, especially to reduce the specular reflection, we shall present an
example based on the FEM technique in two dimensions. The situation is depicted in
Figure 4.18, showing the same three periods of the PRD depicted in Figure 4.17, where
the wells (protrusions) are calculated in Table 4.1.

L

r

S

p

Figure 4.18 Sketch of situation for calculating the sound pressure level above a diffuser surface consisting of
three periods of a primitive root sequence. Height of wells is given in Table 4.1 and height of point source (S) is
0.7 metres.

The resulting sound pressure level from a point source at height 0.7 metres is
calculated on a circle with a radius of 1 metre above the diffuser. As the width of the
wells is chosen equal to 5 cm, there will be a 10 cm flat (hard) surface added to each end
of the diffuser. The calculations were performed using the Comsol Multiphysics™
software, modelling the field outside the semicircle to be a free field by adding a so-
called perfectly matched layer (PML).
The results are shown in Figure 4.19, giving the total sound pressure level, at a
design frequency of 1000 Hz, on the half-circle as a function of angle. The source
acoustic power is arbitrarily set to 1 W, thus giving the rather high sound pressure levels.
The FEM calculations are performed both for the situation described and also for a flat
surface. The results are compared with a simple analytical calculation for an infinitely
large flat surface. Apart from the discrepancies around the main lobe, the FEM
calculations predict the flat surface situation quite well. The most important result,
however, is the effect of the diffuser surface as compared by the flat one, giving a mean
difference in the specular direction in the order of 6–8 dB.

4.7.2 Scattering by objects distributed in rooms

Big industrial halls, either production or assembly spaces, will always contain a large
number of scattering objects. A realistic modelling of the sound propagation in such halls
implies that one has to take scattering phenomena into account. Having objects covering
a wide range of sizes, shapes and orientation in the room one certainly cannot take the
influence of each object into account; one has to rely on rough characterizations and
apply statistical concepts.
In presenting examples on calculating sound propagation in large rooms we shall
use factory halls. It is therefore appropriate to give a short overview on the scattering
theory used, which e.g. is outlined by Kuttruff (1981). Basically, two hypotheses are
used: