Building Acoustics

164 Building acoustics

00S

55.3 55.3

,

4

VV

T

cAcA mV

=⋅=⋅

+

(5.14)

where V is the volume of the room and A is the total equivalent absorption area. The total
absorption area has, as is apparent from last expression, contributions AS from the
surfaces and objects in the room together with the air absorption, the latter specified by
the power attenuation coefficient m.
The determination of the absorption factor is performed by measurements of the
reverberation time before and after the specimen(s) is introduced into the room.
Assuming the specimen to be a plane object having a total surface S (10–12 m^2 ), the
absorption factor is expressed as

(^) Sa
00

55.3 1 1

,

V

cS T T

α

⎛⎞

=−⎜

⎝⎠

⎟ (5.15)

where T and T 0 are the reverberation times in the room with and without the specimen,
respectively. We have assumed that the environmental conditions are the same in both
measurements and furthermore; we have neglected the absorption of the room surface
being covered by the specimen, assuming this to be a hard surface of concrete having
negligible total absorption. However, diffraction effects, denoted earlier on as edge
effects, will often result in obtaining absorption factors in excess of 1.0. This
phenomenon will be treated in more detail below (see section 5.5.3.2). For further details
concerning this method the reader should consult the standard.

5.4 Modelling sound absorbers

Section 5.2 gave an overview of the main types of absorber being used in practice. These
could roughly be divided into two groups: one based on the principle of viscous losses in
a porous medium and the other utilizing a resonance principle. There is, however, no
clear boundary between the two types. In practice, a given product may combine these
two principles and the term used when specifying the absorber may follow the most
dominant feature.
There are several design tools available, certainly of different complexity. Simple
modelling based on lumped elements may often be sufficient, a modelling analogous to
the one used when treating mechanical systems in Chapter 2 (section 2.5.1). An assembly
of elements makes up the actual acoustical system, elements having their analogues in an
equivalent mechanical or electrical system. For the latter, in particular, there are a
substantial number of computer programs that may be applied for calculation on the
analogous acoustical system. One should, however, be warned not to work beyond the
range of validity. Acoustical systems imply wave motion, i.e. using lumped element
models presupposes that the dimensions of the elements must always be less than the
wavelength. Below, we shall give an example on such a modelling technique using a
very simple acoustical system called a Helmholtz resonator.
A step further in modelling acoustical systems, allowing wave motion in one
direction, is by using the transfer matrix method. In the analogous electrical system this
is denoted four-pole theory. The method presupposes that we are able to set up a matrix
that describes the relationship between the acoustical quantities on the input and output
side of each element in the system. The matrices, representing all the elements in the
actual acoustical system, may then be combined to calculate the sought-after quantities.