Handbook for Sound Engineers

182 Chapter 7

(7-54)

A special form of a diffusely reflecting surface can
be realized by lining up phase-grating structures of
varying depths. Based on the effect of coupled O/2
runtime units, these structures produce on the surface a
local distribution of the reflection factor and hence of
the sound particle velocity. Every component of this
velocity distribution produces thereby a sound irradia-
tion into another direction. If according to Schroeder^41
one distributes these reflection factors in accordance
with the maximum sequences of the number theory
(e.g., Barker code, primitive root diffusor PRD,
square-law residual series QRD), and separates these
trough structures from each other by thin wall surfaces,
one obtains diffuse structures of a relatively broadband
effect (up to two and more octaves), Fig. 7-45. With

perpendicular sound incidence, the minimum frequency

limit flow for the occurrence of additional reflection

directions is approximately

(7-55)

where,

c is the velocity of sound in air in m/s (ft/s),

dmax is the maximum depth of structure in m (ft)

Nowadays calculation programs are available to

calculate the scattering coefficients for angle-dependent

sound impact by using Boundary Element Methods,

Fig. 7-46.

Figure 7-43. Example of an acoustically active sawtooth
structure. Measures in mm.

1000

250

1100

160

50

r

b

2

©¹§·---^

2

h

2

+

2 h

= ------------------------

Figure 7-44. Geometrical parameters at structures with

rectangular, triangular, sawtooth-formed, and

cylinder-segment-formed intersection.

Structure Structure Structure Structure

period g width b height h

Rectangle ¾z

   L ¾ z0.2g ¾z0.2g

Isosceles triangle ¾z

   L ¾z0.5g–0.67)g z¾0.25–0.33)g

Sawtooth ¾zL ¾z0.33L

Cylinder segment ¾z

   L ¾ z0.17–1.0)g ¾z0.25–0.5)g

g

h

b

g

h

b

g

h

b

g

h

b

flow

c

2 dmax

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