Page 157 - The Master Handbook Of Acoustics

132 CHAPTER SEVEN

ceiling are involved. All we have done in this low-frequency range is to
measure the decay rate of individual modes, definitely not the average
condition of the room.
We see now why there is that big question mark over applying the
concept of reverberation time to small rooms having dimensions com-
parable to the wavelength of sound. Schultz states that reverberation
time is a statistical concept “in which much of the mathematically
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awkward details are averaged out.” In small rooms these details are
not averaged out.
The reverberation time formulas of Sabine, Eyring, and others are
based on the assumption of an enclosed space in which there is highly
uniform distribution of sound energy and random direction of propa-
gation of the sound. At the low-frequency points of Fig. 7-1, energy is
distributed very unevenly and direction of propagation is far from ran-
dom. After the room was treated, reverberation time measurements
followed the broken line, but statistical randomness still does not pre-
vail below 200 Hz even though modal frequencies are brought under
some measure of control.

Growth of Sound in a Room

Referring to Fig. 7-2A, let us consider a source S and a human receiver
H in a room. As source S is suddenly energized, sound travels outward
from S in all directions. Sound travels a direct path to H and we shall
consider zero time (see Fig. 7-2B) as that time at which the direct
sound reaches the ears of listener H. The sound pressure at H instantly
jumps to a value less than that which left S due to spherical divergence
and small losses in the air. The sound pressure at H stays at this value
until reflection R 1 arrives and then suddenly jumps to the D + R 1 value.
Shortly thereafter R 2 arrives, causing the sound pressure to increase a
bit more. The arrival of each successive reflected component causes
the level of sound to increase stepwise. These additions are, in reality,
vector additions involving both magnitude and phase, but we are
keeping things simple for the purposes of illustration.
Sound pressure at receiver H grows step by step as one reflected
component after another adds to the direct component. The reason
the sound pressure at H does not instantly go to its final value is that
sound travels by paths of varying length. Although 1,130 ft/sec, the