Handbook for Sound Engineers

Computer Aided Sound System Design 1371

each band relative to the target values within a range of

tolerance, Fig. 35-36.

The graph of RT 60 times should allow plotting
multiple RT 60 values within a single graph, so as to
show the impact of various audience sizes, proposed
and/or alternative room treatments, etc., on the RT 60
time. An option must allow plotting a grayed or dashed
area as the desirable range of reverberation times for a
particular project, against which the measured or calcu-
lated RT 60 values can be referenced.

35.3.1.2 Objective Room-Acoustic Measures

The simplest way to obtain objective measures is to use
the direct sound of one or more sources and calculate
the reverberation level of the room by means of the
reverberation time equations assuming the room follows
a statistically even distributed sound decay (homoge-
neous, isotropic diffuse sound field, that is, the RT 60 is
constant over the room). From these calculations it is
possible to derive the direct sound and the diffuse-sound
levels and consequently a range of objective acoustic
parameters, see Section 7.1. It goes without saying that
this requires the acoustical conditions of the room to
show a statistically regular behavior (frequency
response of the reverberation time that is independent of
the location considered in the room). In practice, how-
ever, such behavior will hardly be found. For this reason
one tends to qualify such data as having only a prelimi-
nary guideline character and to have it confirmed by
additional detailed investigations.

35.3.2 Ray Tracing or Image Modeling Approach

35.3.2.1 Preliminary Remark

There are several ways to calculate the impulse

response of a radiated sound event. The widest-known

method is the image-source algorithm. Worth mention-

ing at this point are also the ray-trace method, which

was first known in optics, and other special procedures

like cone tracing or pyramid tracing. Nowadays these

procedures are more often than not used in a combined

form as so-called hybrid procedures.

35.3.2.2 Image Modeling

With image modeling there is a source and a receiving

point selected. Then a deterministic search of all image

sound sources of different orders is started to compute

the impulse response, Fig. 35-37.

In the image modeling method a receiving point is

used instead of a counting balloon (in contrast to clas-

sical ray tracing). Frequency response and interference

effects (including phase investigations) are also easily

calculated.

This method is very time consuming and the calcula-

tion time is proportional to Ni with: N= number of

model walls and i= the order of wall bounces.

Figure 35-36. RT 60 chart with tolerance range.

Figure 35-37. Ray calculation with image model algorithm.

Path S-1-2-L

Source S

Wall 1 Direct path

Path S-2-L

Listener

Path S-1-L

Path S-2-1-L

Image source S’1

1st order

Wall 2

Image source S2

1st order

Image source S”12

Second order

Image Source S”21

second order