Room acoustics - Building Acoustics - page 105

4.2.1 Models for small and large rooms
We have given an overview and some general remarks concerning the different models
used to predict the sound field in rooms. We shall proceed by going into more detail on
the suitability of these models for given situations. Simple diffuse field models may in
practice be quite sufficient predictors given that a certain minimum number of room
modes are being excited and participate in the build-up of the sound field. However,
there are also a number of other conditions that have to be fulfilled before it is reasonable
to assume that a global sound pressure level or a global reverberation time exists. The
linear dimensions of the room must not be too different; the absorption material must be
reasonably evenly distributed on the room surfaces and the total absorption area must not
be too high.
To apply the simple expressions for the reverberation time, given in section 4.5.1.2
below, also presupposes that only the room volume and the total surface area determine
the mean free path of the sound, i.e. the distance between each reflection. When filling
the room with a certain number of scattering objects an “internal” reverberation process
may be set up between these objects and the common reverberation time formulae are no
longer applicable. We should then bear in mind how to explain the diffusing elements
required for laboratories performing standard absorption measurements according to ISO
354. We shall return to this question when treating the subject of scattering.
In conclusion, large discrepancies between the ideal conditions demanded for a
diffuse field and the actual room conditions make such models unsuitable. It may be that
the linear dimensions are quite different; e.g. the room is “flat” in the sense that the
ceiling height is small compared to the length and width of the room (industrial hall,
landscaped office etc.) or the room is “long” (a corridor etc.). Absorbing materials or
objects may also be unevenly distributed and the room may also contain a number of
different types of reflecting and/or scattering object.
The choice of models to use on such “large rooms” is obviously dependent on the
intended function for the room, a function that also determines the parameters we shall
use to validate the acoustic quality. On industrial premises, e.g. large industrial halls,
where a large attenuation between the various noise sources and the workers is aimed at,
the decrease in decibels per metre distance may be a suitable parameter to estimate. For
rooms having a simple shape, such a parameter could be estimated by an analytical
model.
In performance spaces, theatres, auditoria, concert halls etc., the function of the
room is to forward the sound to the audience, which implies that a quite different set of
parameters, are necessary. Predicting the sound field in such rooms is generally based on
methods from geometrical acoustics, partly combined with statistical considerations to
include scattering (diffusion) phenomena. Two methods, principally different, are used:
the ray-tracing method and the mirror-source method. The former simulates a sound
source by emitting a large number of “sound rays”, these being evenly distributed over
the solid angle covered by the actual sound source. Each ray is followed as it hits the
various surfaces in the room, being specularly reflected and radiated having a reduced
energy caused by the absorption factor of the surface.
According to the name, the mirror-source method is based on the mirror images of
the real source. The sound from a mirror source received at a given point is reflected
once in the surface of the mirror. These first-order sources are then being mirrored by all
room surfaces giving second-order sources and so on. Short descriptions of these two
geometrical prediction models are given in section 4.8. Software having implemented
these methods is commercially available. Most of them are based on a hybrid method