Handbook for Sound Engineers

Acoustical Treatment for Indoor Areas 119

number, in this case the square of n, is divided by the
second number, in this case p, and the remainder is equal
to the well depth factor. For example, if n= 5 and p=7,
Eq. 5-9 becomes

25 divided by 7 = 3 with a remainder of 4.

Therefore:

In a similar manner, the well depth factors for all the
other wells are obtained, as shown in Fig. 5-30. Two
complete periods—plus an extra well added to maintain
symmetry—are shown in Fig. 5-30 for a p=7QRD.
Usually the wells are separated by thin, rigid separators
(but not always). An important feature of QRD is
symmetry. This allows them to be manufactured and
utilized in multiple modular forms.
D’Antonio and Konnert have outlined the theory and
application of reflection phase-grating diffusers.^32 The
maximum frequency for effective diffusion is deter-
mined by the width of the wells; the minimum frequency
for effective diffusion is determined by the depth of the
well. Commercial diffusers built on these principles are
available from a variety of manufacturers. RPG, Inc. and
its founder, Dr. Peter D’Antonio, have done pioneering
work in the area of diffusion, particularly with respect to
Schroeder diffusion and, more recently, with
state-of-the-art diffusive surfaces that are customized for
an application through the use of special computer
models and algorithms.

Numerical diffusers such as QRDs can be 1D or 2D

in terms of the diffused sound pattern. QRDs consisting

of a series of vertical or horizontal wells will diffuse

sound in the horizontal or vertical directions, respec-

tively. In other words, if the wells run in the ceiling-floor

direction, diffusion will occur laterally, from side to side,

and the resulting diffusion pattern would resemble a

cylinder. (Incident sound parallel to the wells will be

reflected more than diffused.) More complex numerical

diffusers employ sequences of wells—often elevated

blocks or square-shaped depressions—that vary in depth

(or height) both horizontally and vertically. Incident

sound striking these devices will be diffused in a spher-

ical pattern.

5.3.3 Random Diffusion

Besides numerical diffusers, diffusion can also result

from the randomization of a surface. In theory, these

surfaces cannot provide ideal diffusion. However,

listening to the results after treating the surfaces of a

room with random diffusers would indicate that, subjec-

tively, they perform quite well. Since any randomization

of a surface breaks up specular reflection to some degree,

this is not unexpected. The only limitation will be the

frequency range of significant diffusion. The rules for

well width and depth discussed previously would still

apply, albeit in a general sense since the diffusers will not

have been designed using a formal number theory algo-

rithm. The benefit of random diffusion is that everyday

materials and objects can provide significant diffusion.

For example, bookshelves, media storage shelves, deco-

rative trim or plasterwork, furnishings, fixtures, and other

decorations can all provide some diffusion. This can be

Well depth factor= 25 mod 7

Well depth factor= 25 mod 7

4=

Figure 5-30. A profile of two periods (with one extra well to maintain symmetry) of a QRD of prime number p=7.