180 Chapter 7
Elliptical Effect. If the sound source is located between
half the radius of curvature and the full radius of curva-
ture in front of the reflecting surface, a second sound
concentration point is formed outside the center of curva-
ture, Fig. 7-41B. If this second focus is located within the
performance zone or the audience area, it is perceived as
very disturbing, since distribution of the reflected sound
is very unbalanced. With extended sound sources like an
orchestra, curved surfaces of this kind produce a heavily
register-dependent sound balance.
Parabolic Effect. If in a rather narrow arrangement the
sound source is located at half the center of curvature,
Fig. 7-41C, the curved surface acts like a so-called para-
bolic reflector that generates an axis-parallel bundle of
rays. This produces, on the one hand, a very uniform
distribution of the reflected portion of the sound irradi-
ated by the source, but on the other hand there occurs an
unwanted concentration of noise from the audience area
at the location of the sound source.
Hyperbolic Effect. If the distance of the sound source
from the curved surface is smaller than half the radius
of curvature, Fig. 7-41D, the reflecting sound rays leave
the surface in a divergent fashion. But the divergence is
less and thus the sound intensity at the listener’s seat is
higher than with reflections from a plain surface.^2 The
acoustically favorable scattering effect thus produced is
comparable to that of a convexly curved surface, but the
diverging effect is independent of the distance from the
curved reflecting surface.
7.3.4.3 Sound Reflections at Uneven SurfacesUneven surfaces serve as the secondary structure of
directional or diffuse sound reflections. This refers to
structured surfaces with different geometrical intersec-
tions in the horizontal and vertical planes (rectangles,
triangles, sawtooth, circle segments, polygons) as well
as 3D structures of geometrical layout (sphere
segments, paraboloids, cones, etc.) and free forms
(relievos, moldings, coves, caps, ornaments, etc.). Also
by means of a sequence of varying wall impedances
(alternation of sound reflecting and sound absorbing
surfaces), it is possible to achieve a secondary structure
with scattering effect.
To characterize this sound dispersion of the
secondary structure one makes a distinction between a
degree of diffusivity d and a scattering coefficient s.
Typically for the homogeneity of the distribution of
the sound reflections is the so-called frequency-depen-
dent degree of diffusivity d.^47(7-52)This way angle-dependent diffusion balloons may be
generated. Depending on the number of n receiver posi-
tions hi-res=level values are supplied to form the
balloon.
High diffusion degrees close to one will be reached
for half-cylinder or half-sphere structures. Nevertheless
the diffusion degree d is more or less a qualitative
measure to evaluate the homogeneity of scattering.
On the other side and as a quantitative measure to
characterize the amount of scattered energy in contrast
to the specular reflected or absorbed energy, the
frequency-dependent scattering coefficient s is used.^50
This scattering coefficient s is used in computer
programs to simulate the scattered part of energy espe-
cially by using ray tracing methods.
The coefficient s will be determined as the ratio of
the nonspecular (i.e., of the diffuse reflected) to the
overall reflected energy.(7-53)Figure 7-41. Sound reflection at smooth, curved surfaces.
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