Room acoustics 117
of a resonance. The formula may be understood from the following facts: the resonance
bandwidth is inversely proportional to the reverberation time and the separation between
the eigenfrequencies is inversely proportional to the room volume. For the example used
in Figure 4.3, we arrive at a cut-off frequency of approximately 250 Hz.
In building acoustics, however, we are not normally interested in a statistical
description of pure tone responses for rooms. We shall look for responses averaged over
frequency bands, octave or one-third-octave bands and broadband excitation sources are
used. This leads to a treatment where we are looking at the energy or the energy density
as the primary acoustic variable, which allows us to “forget about” the wave nature of the
field as long as we keep away from the low frequency range. In this relation, it is
pertinent to start by presenting a model that properly may be denoted the classical diffuse
field model. It will appear that the formulae derived from this model are implemented in
a number of measurement procedures both for laboratory and field use, in spite of their
presumptions of an ideal diffuse field. An ideal diffuse field should imply that the energy
density is everywhere the same in the room but, actually, acousticians have agreed
neither on the definition nor on a measurements method for this concept. A couple of
suggestions for a definition:
- In a diffuse field the probability of energy transport is the same in all directions
and the energy angle of incidence on the room boundaries is random. - A diffuse sound field contains a superposition of an infinite number of plane,
progressive waves making all directions of propagation equally probable and
their phase relationship are random at all room positions.
Both definitions, and a number of others, should be conceptually adequate but offer
little help as to the design of a measurement method. We shall not delve into the various
diffusivity measures being suggested, of which none has been generally accepted. In
practice, when the international standards on laboratory measurements are concerned,
procedures on improving the diffusivity are specified together with qualification
procedures to be fulfilled before making the laboratory fit for a certain task. As for
measurements in situ one is certainly forced to accept the existing situation.
In a number of standard measurement tasks in building acoustics, determination of
sound absorption, sound insulation or source acoustic power, the primary tasks is to
determine a time and space averaged squared sound pressure in addition to the
reverberation time. In several cases, pressure measurements may be substituted by
intensity measurements but still averaging procedures in time and over closed surfaces
must be applied. Concerning the measurement accuracy of the averaged (squared)
sound pressure and the reverberation time, this may be predicted using statistical models
for the sound field. We shall return to this topic after treating the classical model for a
diffuse sound field.
4.5.1 Classical diffuse-field model
For the energy balance in a room where a source is emitting a given power W (see Figure
4.7), a simple differential equation may be set up. This power is either “picked up”, i.e.
absorbed, by the boundary surfaces or other objects in the room or contributes to the
build-up of the sound energy density. The boundary surfaces certainly include all
absorbers which may be mounted there. We may write
(^) ()abs
d
,
j j d
w
WWV
t