116 Building acoustics
100 120 140 160 180 200
Frequency(Hz)010203040Relative sound pressure level (dB)Figure 4.6 Some examples of transfer functions measured in an auditorium of volume 1800 m^3. Measurements
by varying the direction of the loudspeaker axis.
4.5 Statistical models. Diffuse-field models
We demonstrated in section 4.4.2 that, rising to sufficiently high frequencies, one cannot
link the various maxima in the transfer functions to the individual eigenfrequencies.
These higher frequency maxima are the result of many, simultaneously excited modes
adding up in phase. Correspondingly, minima in the response are the results of many
modes having amplitudes and phase relationship resulting in a very small vector when
added. It is also very important to realize that the general features of these transfer
functions such as the distribution of minima, the level difference between minima and
maxima, the phase change over a given frequency range etc. is not specifically dependent
on the room or the relative position of the source and receiver. A “flat” frequency
response curve, which is the aim when designing microphones and loudspeakers, will
never be obtained in a room.
At sufficiently high frequencies, however, we may express the abovementioned
variables by statistical means. Specifically, we shall be able to do this when the distance
between the eigenfrequencies becomes less than the bandwidth of the resonances. The
so-called Schroeder cut-off frequency fS, given by
(^) S 2000 ,
T
f
V= (4.22)
where V and T are the volume (m^3 ) and reverberation time (s), respectively, may be used
as a frequency limit above which a statistical treatment is feasible. This corresponds to a
frequency where we will find approximately three eigenfrequencies within the bandwidth