Handbook for Sound Engineers

Acoustical Modeling and Auralization 229

room models that typically do not investigate the distri-

bution of the sound field at the very low frequencies.

9.2.3 Empirical Models

Empirical models are derived from experiments and are
described by equations that typically follow curve-fit-
ting procedures of the data obtained in the observations.
No analytical, geometrical, and/or statistical expression
is developed to fully explain the interdependence of
variables and parameters in the model, but a general
form of a descriptive expression may be constructed
from underlying theories. Empirical models have been
extensively used for many years in acoustical modeling
due to the large quantity of variables and parameters
that are often present when dealing with issues of sound

propagation in a complicated environment, and this sec-

tion will present only a couple of examples.

9.2.3.1 Gypsum Cavity Wall Absorption

There is numerous test data available pertaining to the

sound transmission class (STC) of various wall con-

structions, but little has been investigated regarding the

sound absorption of walls constructed of gypsum (dry-

wall) panels. The absorption of a composite wall panel

is partly diaphragmatic (due to the mounting), partly

adiabatic (due to the porosity of the material and the

air), and some energy is lost inside the cavity via reso-

nance. The complicated absorption behavior of gypsum

walls has been described^18 using an empirical model

that takes into account absorption data acquired in

reverberation chamber experiments. The mathematical

model is fitted to the measured data to account for the

resonant absorption of the cavity by assuming that the

mechanical behavior of the wall can be modeled by a

simple mechanical system.

In this model, the resonance frequency at which the

maximum cavity absorption takes place is given by

(9-15)

where,

m 1 and m 2 are the mass of the gypsum panels

comprising the sides of the wall in kg/m^2 ,

d is the width of the cavity expressed in millimeters,

P is a constant with the following values:

If the cavity is empty (air), P= 1900,

If the cavity contains porous or fibrous sound-absorp-

tive materials, P= 1362.

The empirical model combines the maximum absorp-

tion DMAM taking place at the resonant frequency given

by Eq. 9-15 with the high-frequency absorption DS into a

form that fits data obtained experimentally, to give an

equation that allows for the prediction of the absorption

coefficient of the wall as a function of frequency:

(9-16)

Although it does not take into account all of the

construction variables (stud spacing, bonding between

layers) the model still provides accurate prediction of

the sound absorption parameters of various gypsum

wall constructions.

Figure 9-18. A mapping of the sound field resulting from

modal interference patterns at 34.3 Hz. From CARA.

Figure 9-19. A mapping of the sound field resulting from

modal interference patterns at 54.4 Hz. From CARA.

fMAM P

m 1 +m 2

dm 1 m 2

= ----------------------

D Df (^) MAM
fMAM
f
©¹§·------------
2
= +DMAM