User Guide

Sound System Design Reference Manual
Consider a sound wave striking such a
boundary at normal incidence, shown in Figure 5-4.
The reflected energy leaves the boundary in the
opposite direction from which it entered and
combines with subsequent sound waves to form a
classic standing wave pattern. Particle velocity is
very small (theoretically zero) at the boundary of the
two materials and also at a distance 1/2 wavelength
away from the boundary. Air particle velocity is at a
maximum at 1/4 wavelength from the boundary.
From this simple physical relationship it seems
obvious that unless the thickness of the absorptive
material is appreciable in comparison with a quarter
wavelength, its effect will be minimal.
This physical model also explains the dramatic
increase in absorption obtained when a porous
material is spaced away from a boundary surface.
By spacing the layer of absorptive material exactly
one-quarter wavelength away from the wall, where
particle velocity is greatest, its effective absorption is
multiplied many times. The situation is complicated
by the necessity of considering sound waves arriving
from all possible directions. However, the basic effect
remains the same: porous materials can be made
more effective by making them thicker or by spacing
them away from non-absorptive boundary surfaces.
A thin panel of wood or other material also
absorbs sound, but it must be free to vibrate. As it
vibrates in response to sound pressure, frictional
losses change some of the energy into heat and
sound is thus absorbed. Diaphragm absorbers tend
to resonate at a particular band of frequencies, as
any other tuned circuit, and they must be used with
care. Their great advantage is the fact that low
frequency absorption can be obtained in less depth
than would be required for porous materials. See
Figure 5-5.
A second type of tuned absorber occasionally
used in acoustical work is the Helmholtz resonator: a
reflex enclosure without a loudspeaker. (A patented
construction material making use of this type of
absorption is called “Soundblox”. These masonry
blocks containing sound absorptive cavities can be
used in gymnasiums, swimming pools, and other
locations in which porous materials cannot be
employed.)
The Growth and Decay of a Sound Field
in a Room
At this point we should have sufficient
understanding of the behavior of sound in free space
and the effects of large boundary surfaces to
understand what happens when sound is confined in
an enclosure. The equations used to describe the
behavior of sound systems in rooms all involve
considerable “averaging out” of complicated
phenomena. Our calculations, therefore, are made
on the basis of what is typical or normal; they do not
give precise answers for particular cases. In most
situations, we can estimate with a considerable
degree of confidence, but if we merely plug numbers
into equations without understanding the underlying
physical processes, we may find ourselves making
laborious calculations on the basis of pure
guesswork without realizing it.
Suppose we have an omnidirectional sound
source located somewhere near the center of a
room. The source is turned on and from that instant
sound radiates outward in all directions at 344
meters per second (1130 feet per second) until it
strikes the boundaries of the room. When sound
strikes a boundary surface, some of the energy is
absorbed, some is transmitted through the boundary
and the remainder is reflected back into the room
where it travels on a different course until another
reflection occurs. After a certain length of time, so
many reflections have taken place that the sound
field is now a random jumble of waves traveling in all
directions throughout the enclosed space.
If the source remains on and continues to emit
sound at a steady rate, the energy inside the room
builds up until a state of equilibrium is reached in
which the sound energy being pumped into the room
from the source exactly balances the sound energy
dissipated through absorption and transmission
through the boundaries. Statistically, all of the
individual sound packets of varying intensities and
varying directions can be averaged out, and at all
points in the room not too close to the source or any
of the boundary surfaces, we can say that a uniform
diffuse sound field exists.
The geometrical approach to architectural
acoustics thus makes use of a sort of “soup” analogy.
As long as a sufficient number of reflections have
taken place, and as long as we can disregard such
anomalies as strong focused reflections, prominent
resonant frequencies, the direct field near the
source, and the strong possibility that all room
surfaces do not have the same absorption
characteristics, this statistical model may be used to
describe the sound field in an actual room. In
practice, the approach works remarkably well. If one
is careful to allow for some of the factors mentioned,
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