User Guide

Sound System Design Reference Manual
Suppose we place a small non-directional
sound source in a room having R = 200 m
2
. If we
measure the sound level at a distance 0.25 meter
from the acoustic center and then proceed to walk in
a straight line away from the source, the level will at
first decrease as the square of the distance. However,
about 1 meter from the source, the inverse square
relationship no longer applies. At distances of 6 meters
or more from the source, there is no substantial
change in sound pressure at all because we are well
into the reverberant field and the direct sound no
longer has a perceptible effect upon our reading.
If we reverse our path and walk back toward
the source from a distance of 12 or 15 meters, sound
pressure at first remains unchanged and then
gradually begins to climb until, at a distance about 2
meters from the source, it has increased 3 dB above
the reverberant field reading. This position, indicated
by the mark on the curve, is the critical distance.
The graph of Figure 5-20 is a universal
relationship in which critical distance is used as the
measuring stick. It can be seen that the effective
transition zone from the reverberant field to the direct
field exists over a range from about one-half the
critical distance to about twice the critical distance. At
one-half the critical distance, the total sound field is 1
dB greater than the direct field alone; at twice the
critical distance, the total sound field is 1 dB greater
than the reverberant field alone.
The ratio of direct to reverberant sound can be
calculated from the simple equation shown below the
chart, or estimated directly from the chart itself. For
example, at four times D
C
the direct sound field is 12
dB less than the reverberant sound field. At one-half
D
C
, the direct sound field is 6 dB greater than the
reverberant sound field.
Remember that, although critical distance
depends on the directivity of the source and the
absorption characteristics of the room, the
relationships expressed in Figure 5-19 remain
unchanged. Once D
C
is known, all other factors can
be calculated without regard to room characteristics.
With a directional sound source, however, a given
set of calculations can be used only along a specified
axis. On any other axis the critical distance will
change and must be recalculated.
Let us investigate these two factors in some
detail: first the room constant R, and then the
directivity factor Q.
We have already mentioned that the room
constant is related to the total absorption of an
enclosed space, but that it is different from total
absorption represented by Sα.
One way to understand the room constant is
first to consider that the total average energy density
in a room is directly proportional to the power of the
sound source and inversely proportional to the total
absorption of the boundary surfaces. This
5-16
Figure 5-20. Relative SPL vs. distance from source in relation to critical distance