Handbook for Sound Engineers

178 Chapter 7

reflection from sound sources on the stage. Convex
curves (in the vertical domain) combined with a
sound-absorbing effect in the low-frequency range are,
in this respect, especially advantageous for making the
supporting effect register-independent on the one hand
and brilliance enhancing on the other hand. The edge of
the stage above the pit vis-à-vis the conductor should be
conformed geometrically in such a way that additional
initial reflections are directed to the audience area. The
lateral configuration of the pit opening, combined with
an appropriate subconstruction of the proscenium side
wall, should insure a maximum of sound reflections
towards the pit and the stage.

7.3.4 Secondary Structure of Rooms

7.3.4.1 Sound Reflections at Smooth Plane Surfaces

With the reflection of sound rays from boundary
surfaces, one can principally define three types of
reflection which differ from one another by the relation
between the linear dimensions and the wavelength and
by the relation between the reflected and the incident
sound ray, Fig. 7-37.

• Geometrical reflection, Fig. 7-37A: b<O, D=ß
  (specular reflection according to the reflection law in
  one plane perpendicular to the carrier wall).


• Directed (local) reflection, Fig. 7-37B: b>O, D=ß
  (specular reflection according to the reflection law,
  referred to the effective structural surface).


• Diffuse reflection, Fig. 7-37C: b|O, (no specular
  reflection, without a preferred direction).

A geometrical sound reflection occurs at a suffi-
ciently large surface analogously to the reflection law of
optics: the angle of incidence D is equal to the angle of
reflection ß and lies in a plane perpendicular to the
surface, Fig. 7-38. This reflection takes place only down
to a lower limit frequency flow

(7-51)

where,
c is the velocity of sound in air.

Below flow the sound pressure level decay amounts to
6 dB/octave.^38
Eq. 7-51 has been graphically processed, Fig. 7-39.^3
With a reflector extension of 2 m (6.6 ft) at a distance of
10 m (3 ft) each from the sound source and to the
listener, the lower limiting frequency is, for example,

about 80 Hz with vertical sound incidence and about

1600 Hz with an incidence angle of 45°. If this reflector

is installed as a panel element in the front part of the

platform, the frequency region of the sound reflections

is about one octave lower with almost platform-parallel

arrangement than in a 45° inclined position. The desired

limiting frequency goes down to lower values under the

following circumstances:

• The bigger the effective surface.


• The nearer to the sound source and to the listener the
  reflector is installed.


• The smaller the sound incidence angle.

Apart from the geometry of the reflectors, the

area-related mass of the same also has to be consistent

with certain limit values in order to obtain a reflection

with as little a loss as possible. If the reflectors are

employed for speech and singing in the medium and

high-frequency ranges, a mass of about 10 kg/m^2

(1.7 lbs/ft^2 ) is sufficient (e.g. a 12 mm (½ in) plywood

plate). If the effective frequency range is expanded to

bass instruments, a mass of about 40 kg/m^2 (1.7 lbs/ft^2 )

has to be aspired (e.g., 36mm [1.5 in] chipboard). With

reflectors additionally suspended above the perfor-

mance zone, the statically admissible load often plays a

flow^2 c

bcosD^2

-----------------------

a 1 a 2

a 1 +a 2

= u-----------------

Figure 7-37. Basic sound reflections at smooth, plane

surfaces.

A

A

B

B

b > LAB

directed reflection

b L

diffuse reflection

b

A

A

B

B

b < LAB

geometrical reflection

A.

B.

C.

~~