User Guide

Sound System Design Reference Manual
More recent publications usually express the
absorption in an enclosed space in terms of the
average absorption coefficient . For example, if a
room has a total surface area of 1000 square meters
consisting of 200 square meters of material with an
absorption coefficient of .8 and 800 square meters of
material with an absorption coefficient of .1, the
average absorption coefficient for the entire internal
surface area of the room is said to be .24:
Area: Coefficient: Sabins:
200 x 0.8 = 160
800 x 0.1 = 80
1000 240
α = 240 = 0.24
1000
The use of the average absorption coefficient α
has the advantage that it is not tied to any particular
system of measurement. An average absorption
coefficient of 0.15 is exactly the same whether the
surfaces of the room are measured in square feet,
square yards, or square meters. It also turns out that
the use of an average absorption coefficient
facilitates solving reverberation time, direct-to-
reverberant sound ratio, and steady-state sound
pressure.
Although we commonly use published
absorption coefficients without questioning their
accuracy and perform simple arithmetic averaging to
compute the average absorption coefficient of a
room, the numbers themselves and the procedures
we use are only approximations. While this does not
upset the reliability of our calculations to a large
degree, it is important to realize that the limit of
confidence when working with published absorption
coefficients is probably somewhere in the
neighborhood of ±10%.
How does the absorption coefficient of the
material relate to the intensity of the reflected sound
wave? An absorption coefficient of 0.2 at some
specified frequency and angle of incidence means
that 20% of the sound energy will be absorbed and
the remaining 80% reflected. The conversion to
decibels is a simple 10 log function:
10 log
10
0.8 = -0.97 dB
In the example given, the ratio of reflected to
direct sound energy is about -1 dB. In other words,
the reflected wave is 1 dB weaker than it would have
been if the surface were 100% reflective. See the
table in Figure 5-3.
Thinking in terms of decibels can be of real help
in a practical situation. Suppose we want to improve
the acoustics of a small auditorium which has a
pronounced “slap” off the rear wall. To reduce the
intensity of the slap by only 3 dB, the wall must be
surfaced with some material having an absorption
coefficient of 0.5! To make the slap half as loud (a
reduction of 10 dB) requires acoustical treatment of
the rear wall to increase its absorption coefficient to
0.9. The difficulty is heightened by the fact that most
materials absorb substantially less sound energy
from a wave striking head-on than their random
incidence coefficients would indicate.
Most “acoustic” materials are porous. They
belong to the class which acousticians elegantly
label “fuzz”. Sound is absorbed by offering resistance
to the flow of air through the material and thereby
changing some of the energy to heat.
But when porous material is affixed directly to
solid concrete or some other rigid non-absorptive
surface, it is obvious that there can be no air motion
and therefore no absorption at the boundary of the
two materials.
Figure 5-3. Reflection coefficient in decibels
as a function of absorption coefficient
5-3