User Guide

Sound System Design Reference Manual
We can agree that if the source of sound in a
given room is non-directional, the equation for R is
probably accurate for all practical purposes. It would
also seem that the equation could be used for a
room in which absorption was uniformly distributed
on all boundary surfaces, regardless of the directivity
of the source. Where we run into trouble is the
situation of a directional source and absorption
concentrated in restricted areas. The description is
exactly that of a classical concert hall in which almost
all absorption is provided in the audience area and in
which the sound system designer has endeavored to
concentrate the power from the loudspeakers directly
into the audience.
One could go through laborious calculations to
arrive at the intensity of the reverberant field by
taking reflections one by one. In practice, however, it
is usually sufficient to make an educated guess as to
the amount of energy absorbed in the first reflection.
We can denote the absorption coefficient of this first
reflection as α ’ . The energy remaining after the first
reflection must then be proportional to (1 - α’). This
allows us to write an expression for the effective
room constant designated by the symbol R’ :
R’ = Sα/(1 - α’).
The importance of determining the room
constant as accurately as possible lies in the fact that
it not only allows us to calculate the maximum level
of a given sound system in a given room, but also
enters into our calculations of critical distance and
direct-to-reverberant sound ratio.
Although not explicitly stated, R’ can be used in
any of the equations and charts in which the room
constant appears, Figures 5-19, 21, and 22, for
example. In most situations, the standard equation
for R will seem to be a reasonable approximation of
the condition that exists. In each case, however, an
examination of the room geometry and source
directivity should be made, and the designer should
try to estimate what will really happen to the sound
energy after the first reflection.
Figures 5-21 and 5-22 present some
reverberant field relationships in graphical form. For
example, if we know the efficiency of a sound source,
and hence its acoustical power output in watts, we
can measure the sound pressure level in the
reverberant field and determine the room constant
directly. Or, if the room is not accessible to us, and a
description of the room enables us to estimate the
5-18
Figure 5-22. Room constant vs. surface area and α