Handbook for Sound Engineers

Acoustics for Auditoriums and Concert Halls 181

The measurement and calculation of the scattering
coefficient under random sound impact take place in the
reverberation chamber.39,48,49
All these parameters don’t say too much about the
angular distribution of the reflected sound energy. But
there exist many examples of rooms in which the
secondary structure is intended to realize a directional
reflection in which the angle of sound reflection does
not correspond to the angle of sound incidence, as
referred to the basic surface underlying the primary
structure. In this case of directional sound reflection,
one has to consider parameters determining, among
other things, the diffusivity ratio Ddiff and the maximum
displacement dD, Fig. 7.42.^42

• Diffusivity ratio Ddiff : sound pressure level difference
  between the directional and the diffuse sound compo-
  nents Lmax and Ldiff, respectively.
  o Characterizes the directional effect of a structure.


• Attenuation of Maximum 'amax: sound pressure level
  difference between the directional reflection (local
  maximum, ßmax) of the structure, as compared with a
  plain surface.
  o Characterizes the sound pressure level of the
  reflection.


• Displacement of Maximum dD: angle between geo-
  metrical and directional reflections.
  o Characterizes the desired change of direction of
  the reflection.


• Angular range of uniform irradiation 'D: 3 dB band-
  width of the reflection.
  o Characterizes the solid-angle range of uniform
  sound reflection.

Guide values Ddiff for the octave midband frequency
of 1000 Hz are based on subjective sound-field investi-
gations in a synthetic sound field, Table 7-9.

An example for a sawtooth structure is shown in Fig.

7-43. This side wall structure has at a sound incidence

angle of 50° and a speech center frequency of about

1000 Hz, energy-rich directional sound reflections

(Ddifft10 dB) with a displacement of maximum of

dD=20° (reflection angle 30°). Additionally direc-

tional and diffuse sound components being perceptible

from about 3000 Hz (Ddiff= 6 to 8 dB). The attenuation

of maximum 'amax was 5 dB at 1000 Hz and 11 dB at

5000 Hz by comparison with a carrier panel of geomet-

rical sound reflection.

Periodical structures of elements having a regular

geometrical cut (rectangle, isosceles triangle, sawtooth,

cylinder segment) may show high degrees of scattering,

if the following dimensions are complied with,

Fig. 7-44.3,40

For a diffuse scattering in the maximum of the

speech-frequency range, the structure periods are there-

fore about 0.6 m (2 ft), the structure widths between 0.1

to 0.4 m (0.33 to 1.3 ft), and the structure heights maxi-

mally about 0.3 m (1 ft). With rectangular structures the

sound scattering effect is limited to the relatively small

band of about one octave, with triangular structures to

maximally two octaves. Cylinder segments or geomet-

rical combinations can favorably be used for more

broadband structures, Fig. 7-43. In a wide-frequency

range between 500 Hz and 2000 Hz, a cylinder segment

structure is sufficiently diffuse, if the structure width of

about 1.2 m (4 ft) is equal to the structure period, and

the structure height is between 0.15 and 0.20 m (0.5 and

0.7 ft). With a given structure height h and a given

structure width b it is, according to Eq. 7-54, possible to

calculate the required curvature radius r as

Figure 7-42. Parameters for characterizing the directivity of
uneven surfaces.

Table 7-9. Perception of Diffuse and Directed Sound

Reflections as a Function of the Diffusivity Ratio Ddiff

Perception Ddiff in

dB

Ideal diffuse sound reflection 0

Diffuse sound reflection < 3

Range of appropriate perception of diffuse and directed

sound reflections

3–10

RT around 1.0 s with energy-rich ceiling reflections 2–6

RT around 2.0 s with energy-rich ceiling reflections 4– 8

Spatial sound fields with low direct sound energy,

but big part of lateral reflections

6– 8

Sound fields with high direct sound energy—e.g.,

more distant listener groups

3– 6

Low sound energy of ceiling reflections and big part

of lateral sound

8–10

Directed sound reflection >10

Ideal directed sound reflection f