Introduction to Acoustics

314 Part C Architectural Acoustics
Part C 9.4
if the empty–occupied difference in T is limited to 0.2s,
as suggested here, then the difference in these parameters
will be fairly limited, with changes in both C and G
being less than one dB - given that the audience does
not introduce additional grazing incidence attenuation
of direct sound and early reflections (Sect. 9.6.2).
For opera, one may aim towards the same relationships
between the diffuse field expected and the desired
values of EDT, C and G, as mentioned above for symphonic
halls; but the goal for the reverberation time will
normally be set somewhat lower, 1.4–1.8 s in order to
obtain a certain intelligibility of the libretto and perhaps
to make breaks in the music sound more dramatic
(Sect. 9.7.2).
For rhythmic music, T values of 0.8–1.5 s, depending
on room size, are appropriate, and certainly the value
should not increase towards low frequencies in this case.
9.4 Measurement of Objective Parameters
Whenever the acoustic specifications of a building are
of importance we need to be able to predict the acoustic
conditions during the design process as well as document
the conditions after completion. Therefore, in this and
the following sections, techniques for measurement and
prediction of room acoustic conditions will be presented.
In Sect. 9.2.1 it was claimed that the impulse response
contains all relevant information about the acoustic
conditions in a room. If this is correct, it must also be
true that all relevant acoustic parameters can be derived
from impulse response measurements. Fortunately, this
has also turned out to be the truth.
9.4.1 The Schroeder Method
for the Measurement of Decay Curves
Originally, reverberation decays were recorded from the
decay of the sound level following the termination of
a stationary sound source. However, Schroeder [9.15]
has shown that the reverberation curve can be measured
with increased precision by backwards integration of the
impulse response, h(t), as follows:
�∞
R(t) = h 2 �∞
(t)dt = h 2 �
(t)dt −
t
0
0
t
h 2 (t)dt (9.20)
in which R(t) is equivalent to the decay of the squared
pressure decay. The method is called backwards integration
because the fixed upper integration limit,
infinite time, is not known when we start the recording.
In very large rock venues such as sports arenas, it may
actually be very difficult to get T below 3–5 s; but even
then the conditions can be satisfactory with a properly
designed sound system. The reason is that in such large
room volumes the level of the reverberant sound can often
be controlled, if highly directive loudspeakers are
being used. In these spaces, the biggest challenge is
often to avoid highly delayed echoes, which are very annoying.
For amplified music, only recommendations for
T are relevant, because the acoustic aspects related to
the other parameters will be determined primarily by the
sound system (Sect. 9.7.5).
In order to ensure adequate speech intelligibility in
lecture halls and theaters, values for STI/RASTI should
be at least 0.6. In reverberant houses of worship values
higher than 0.55 are hard to achieve even with a welldesigned
loudspeaker system.
Therefore, in the days of magnetic tape recorders, the integration
was done by playing the tape backwards. In this
context infinite time means the duration of the recording,
which should be comparable with the reverberation
time. Traditional noise decays contain substantial, random
fluctuations because of interference by the different
eigenmodes present within the frequency range of the
measurement (normally 1/3 or 1/1 octaves). These fluctuations
will be different each time the measurement is
carried out because the modes will be excited with random
phase by the random noise (and the random time
of the noise interruption). When, instead, the room is
exited by a repeatable impulse, the response will be repeatable
as well without such random fluctuations. In
fact, Schroeder showed that the ensemble average of
interrupted noise decays (recorded in the same source
and receiver positions) will converge towards R(t)asthe
number of averages goes towards infinity.
In (9.20), the right-hand side indicates that the impulse
response decay can be derived by subtracting the
running integration (from time zero to t) from the total
energy. Contrary to the registration of noise decays,
this means that the entire impulse response must be
stored before the decay function is calculated. However,
with modern digital measurement equipment, this
is not a problem. From the R(t) data, T is calculated
by linear regression as explained in Sect. 9.3.1. Asthe
EDT is evaluated from a smaller interval of the decay
curve than T, theEDT is more sensitive to random decay
fluctuations than is T. Therefore, EDT should never