User Guide

Sound System Design Reference Manual
Rather than go through the calculations, it is
much faster to use a simple chart. Charts calculated
from the Eyring formula are given in Figures 5-10
and 5-11. Using the chart as a reference and again
checking our hypothetical example, we find that a
room having a mean free path just a little less than 3
meters and an average absorption coefficient of .2
must have a reverberation time of just a little less
than .5 seconds.
Since reverberation time is directly proportional
to the mean free path, it is desirable to calculate the
latter as accurately as possible. However, this is not
the only area of uncertainty in these equations. There
is argument among acousticians as to whether
published absorption coefficients, such as those of
Figure 5-12, really correspond to the random
incidence absorption implicit in the Eyring equation.
There also is argument over the method used to find
the “average” absorption coefficient for a room. In our
example, we performed a simple arithmetic
calculation to find the average absorption coefficient.
It has been pointed out that this is an unwarranted
simplification — that the actual state of affairs
requires neither an arithmetic average nor a
geometric mean, but some relation considerably
more complicated than either.
Another source of uncertainty lies in
determining the absorption coefficients of materials in
situations other than those used to establish the
rating. We know, for example, that the total
absorption of a single large patch of material is less
than if the same amount of material is spread over a
number of separated, smaller patches. At higher
frequencies, air absorption reduces reverberation
time. Figure 5-13 can be used to estimate such
deviations above 2 kHz.
A final source of uncertainty is inherent in the
statistical nature of the model itself. We know from
experience that reverberation time in a large concert
hall may be different in the seating area than if
measured out near the center of the enclosed space.
With all of these uncertainties, it is a wonder
that the standard equations work as well as they do.
The confidence limit of the statistical model is
probably of the order of 10% in terms of time or
decay rate, or ±1 dB in terms of sound pressure
level. Therefore, carrying out calculations to 3 or 4
decimal places, or to fractions of decibels, is not only
unnecessary but mathematically irrelevant.
Reverberation is only one of the characteristics
that help our ears identify the “acoustical signature”
of an enclosed space. Some acousticians separate
acoustical qualities into three categories: the direct
sound, early reflections, and the late-arriving
reverberant field.
5-11
Figure 5-13. Effect of air absorption on calculated reverberation time