150 Building acoustics
In more recent time, the practical use of such analytical models is certainly reduced
due to powerful computer simulations, either based on the ray-tracing or the image-
source technique. The purpose of bringing forward the above works is primarily to
illustrate some of the fundamental principles behind this type of modelling.
4.8.3 The model of Ondet and Barbry
An interesting solution to the problem of including scattering object was given by Ondet
and Barbry (1989), which was implemented in the computer program RAYSCAT
(RAYCUB in a later version). This is not, as the models discussed above, an image-
source model but a ray-tracing one. Therefore, it does not impose any restrictions as to
the shape of the room like the analytical models. The idea is to regard the areas of the
room that contain scattering objects as zones having mean free paths depending on the
density of these objects (see Figure 4.21). Each of these zones is allocated a certain mean
free pathRR= k, where the index k indicates the actual zone, whereas the areas without
scattering object are allocated a mean free path R=∞.How is this idea compatible with
a ray-tracing model where one certainly has to follow each ray around in the room?
Ondet and Barbry start by again using the Poisson distribution given by Equation
(4.70), and they show that the paths lengths Ri covered between each hit have a
probability density distribution given by
PR q()=⋅e ,−qR (4.82)which gives an expected value E{RR q}==1/.Furthermore, one may generate these
random distances Ri by using random numbers ai between zero and one, thereafter
inserting these numbers into the following expression:
RRai=− ⋅ln( ).i (4.83)
The procedure is then as follows: One follows each ray in the normal manner until it
crosses the border of a zone defined to contain scattering objects and thereby allocated a
certain mean free path. A path length R 1 is then computed according to Equation (4.83)
by drawing a random number a 1. This implies that it hits a scattering object after
covering the distance R 1 , thereafter directed in a random direction with a new random
path length R 2. It may then hit another object within this zone or maybe escape from this
zone.
A good fit between measured and predicted results is obtained by applying this
procedure, both by Ondet and Barbry (1988) and others (see e.g. Vermeir (1992)). The
computing time may, however, be quite long for rooms having complicated shapes, many
zones with scattering objects of high density.
Later, other models have been developed (see e.g. Dance and Shield (1997)),
limiting the room shape to rectangular where one may easily implement an image-source
model, however, trying to keep the most important concepts from the Ondet–Barbry
model; i.e. the subdivision of the room into zones containing scattering objects, the
placement of absorbing element and barriers etc. The program CISM by Dance and
Shield gives shorter computing times but at the expense of accuracy. It is not able to
represent scattering in the same manner as the models treated above, which decreases the
accuracy in areas far from the nearest source.