Page 166 - The Master Handbook Of Acoustics

141
REVERBERATION

scale. The number of modes included within an octave band centered
on 63 Hz in the specific case to be elaborated later is as follows: 4 axial,
6 tangential, and 2 oblique modes between the –3-dB points. These are
graphically shown in Fig. 7-7 in which the taller lines represent the
more potent axial modes, the intermediate height the tangential
modes, and the shorter lines the oblique modes.
As the switch of Fig. 7-6 is closed, the high-level random noise from
the loudspeaker energizes the various modes of the room, exciting
mode A, and an instant later exciting mode B. While the shift is being
made in the direction of mode B, mode A begins to decay. Before it
decays very far, however, the random-noise instantaneous frequency is
once more back on A, giving it another boost. All the modes of the room
are in constant agitation, alternating between high and somewhat lower
levels, as they start to decay in between kicks from the loudspeaker.
At what point will this erratic dance of the modes be as the switch
is opened to begin the decay? It is strictly a random situation, but it
can be said with confidence that each time the switch is opened for
five successive decays, the modal excitation pattern will be some-
what different. The 12 modes in the 63-Hz octave will all be highly
energized, but each to a somewhat different level the instant the
switch is opened.

Octave centered on 63 Hz

0 20 40 60 80 100
Frequency - hertz
FIGURE 7-7

The normal modes included (–3 dB points) in an octave centered on 63 Hz. The tallest
lines axial modes, the intermediate length tangential modes, and the shortest ones
oblique modes.