1266 Chapter 34
the design of a complex cluster, but only when all room
and loudspeaker data is accurate. In any case, the
complexity of the design process and the economic
consequences of errors are significant enough that the
services of an experienced, qualified acoustical consul-
tant are highly recommended.
34.3.2.10.1 The Fundamental Complexity
When a cluster involves more than perhaps two or three
loudspeakers, its operation becomes complex. The cal-
culation of Alcons for a far-throw loudspeaker, for exam-
ple, cannot ignore the reverberant field contributions
from the other loudspeakers in the cluster. A qualitative
method of dealing with the problem is straightforward.
The direct sound level at each listener can be calculated
via the inverse-square law, Eq. 34-1, from a knowledge
of which loudspeaker or loudspeakers are aimed at the
listener. The total reverberant field sound pressure level
can be calculated by adding the total acoustic power out-
put of all the loudspeakers and placing this value into a
modified form of the room reverberation equation.
Answering the four questions becomes a matter of using
either the direct sound, the direct plus reverberant sound,
or a direct/reverberant ratio.5,6
Calculating the reverberant field level in the room
requires a detailed knowledge of the room’s acoustic
parameters, however, and in many rooms, the acoustic
parameters change from position to position in the
room. A religious facility in the shape of a cross (cruci-
form church), with balconies in each wing, for example,
may have several totally acoustically different spaces
that can be covered from the same cluster location.
While each space has different acoustics, they interact
with each other in a complex way further complicating
the process of calculating the reverberant field at any
listener’s location, Fig. 34-23.
Even in rooms that are fairly well behaved acousti-
cally and have a statistically random reverberant field,
the calculation of reverberant field level is not simple.
This is because this calculation requires a thorough
knowledge of the characteristics of the cluster. Each
loudspeaker adds an amount to the reverberant field that
depends on the electrical power applied to the loud-
speaker and its efficiency. While few manufacturers
provide direct data on the efficiency of their loud-
speakers, this can be calculated from a knowledge of the
on-axis sensitivity and the Q.
Finally, all the factors involved in the reverberant
field calculation vary with frequency so that, for full
precision, a new set of calculations must be performed
for each frequency of interest.34.3.2.10.2 Simplifying the Complex Cluster Design
ProcessBefore the advent of EASE, Modeler and the earlier
software design tools, these complexities were so over-
whelming that few designers made any attempt to deal
with them directly. Instead, they used simplifications
such as the Dc Modifier approach. This approach
involves calculating a value of N for the cluster.
A simple estimate of N is the total number of loud-
speakers producing the same acoustic power as the
loudspeaker pointed at any given listener. For example,
if there are three loudspeakers in the system, all
producing the same acoustic power, and only one loud-
speaker is pointed at the listener, then N equals 3. If
there are four loudspeakers, two of which are pointed at
the listener, the situation is the same as having two
loudspeakers with one pointed at the listener. Therefore,
N would equal 2.
It’s possible to extend this simple estimate in a
logical manner resulting in a value of N for almost any
cluster. However, the process itself is complex and it
depends on estimates for the acoustic power output of
each loudspeaker calculated from the loudspeaker’s
published Q and Ls, both of which are compromise
values that vary with frequency.
A better way is to rely on a software evaluation of
the complex cluster performed by EASE or Modeler or
one of the other software design tools. The detailed
loudspeaker data required by these software tools
enables them to calculate the acoustic power output of
each loudspeaker and, thus, its contribution to the rever-Figure 34-22. A large, complex cluster. Courtesy JBL
Professional.