Page 231 - The Master Handbook Of Acoustics

206 CHAPTER NINE

at 63 Hz (which would be of interest in music recording studios). Dry-
wall absorption in small audio rooms is free; you just have to recognize
its existence and remember to include its low-frequency absorption in
calculations.
The simplest resonant type of absorber utilizes a diaphragm vibrat-
ing in response to sound and absorbing some of that sound by fric-
tional heat losses in the fibers as it flexes.
1
A piece of 4″ plywood is an excellent example. Assume that it is
spaced out from the wall on two-by-fours, which gives close to 3 4″
3
airspace behind. The frequency of resonance of this structure can be
calculated from the expression:

170
f (9-3)
o
(m) (d )
where
f frequency of resonance, Hz
o
m surface density of the panel, lb/sq ft of panel surface
d depth of airspace, inches.
1
The surface density of 4″ plywood, 0.74 lb/sq ft, can be measured
or found in the books. Substituting in Eq. 9-3 we get:
170
f
o
(0.74) (3.75 )
f 102 Hz
o
Figure 9-21 is a graphical solution of Eq. 9-3 for maximum conve-
nience. Knowing only the thickness of the plywood and the depth of
the space behind the plywood, the frequency of resonance can be read
off the diagonal lines. Equation 9-3 applies to membranes and
diaphragms of materials other than plywood such as masonite, fiber-
board, or even Kraft paper. For other than plywood, the surface density
must be determined. The surface density is easily found by weighing a
piece of the material of known area.
How accurate are Eq. 9-3 and Fig. 9-21? Actual measurements on
three plywood membrane absorbers are shown in Fig. 9-22. Such cal-
culations of the frequency of peak absorption at resonance are not per-
fect, but they are a good first approximation of sufficient accuracy for
most purposes.