Handbook for Sound Engineers

Acoustics for Auditoriums and Concert Halls 185

• The clear spacing of the coffering should be, in
  general, smaller in every direction than 0.5 times the
  wavelength in case of resonance, but not fall short of
  0.5 m (1.7 ft).


• The minimum size of the vibrating panel must not
  fall short of 0.4 m^2 (4.3 ft^2 ).


• The air-space damping material should be attached to
  the solid wall so that the panel vibration is not
  impaired in any way.


• The sound absorption coefficient depends on the Q
  factor of the resonance circuit and amounts at the res-
  onance frequency to between 0.4 and 0.7 with
  air-cushion damping and to between 0.3 and 0.4
  without air-cushion damping. At an interval of one
  octave from the resonance frequency one must
  reckon that the sound absorption coefficient is
  halved.

An effective method for increasing the acoustically
effective resonance frequencies of panel resonators
consists of reducing the vibrating mass of heavy panels
by means of holes arranged in defined patterns. In this
case the correlations are governed by analogous regular-
ities, if the area-related mass mc of the panels is replaced
by the effective hole mass mcL. For circular holes of
radius R and a hole-surface ratio H Fig. 7-48, the hole
mass is calculated as

(7-67)

where,
mcL is the area-related air mass of circular openings in
kg/m^2 (lb/ft^2 ),
l* is the effective panel thickness with due consider-
ation of the mouth correction of circular openings of
radius R in meters (ft)

, (7-68)

is the hole-area ratio according to Fig. 7-47 for

circular openings

. (7-69)

Provided the hole diameters are sufficiently narrow,

the damping material layer arranged between the perfo-

rated panel and solid wall can be replaced by the friction

losses produced in the openings. By using transparent

materials—e.g., glass—it is possible to fabricate opti-

cally transparent, so-called micro-perforated absorbers.

The diameters of the holes are in the region of 0.5 mm

(0.02 in) with a panel thickness of 4 to 6 mm (0.16 to

0.24 in) and a hole-area ratio of 6%. For obtaining

broadband sound absorbers, it is possible to resort to

variable perforation parameters (e.g., scattered perfora-

tion) varying thickness of the air cushion and composite

absorbers combined of various perforated panels.

A very recent development are microperforated foils

of less than 1 mm (0.04 in) thickness which also produce

remarkable absorption when placed in front of solid

surfaces. The transparent absorber foil can be advanta-

geously arranged in front of windows either fixed or also

as roll-type blinds in single or double layer.^44

7.3.4.4.3 Helmholtz Resonators

Helmholtz resonators are mainly used for sound absorp-

tion in the low-frequency range. Their advantage, as

compared with panel absorbers (see Section 7.3.4.4.2),

lies in their posterior variability regarding resonance

frequency and sound absorption coefficient as well as in

the utilization of existing structural cavities which must

not necessarily be clearly visible. According to Fig.

7-49, a Helmholtz resonator is a resonance-capable

spring-mass system which consists of a resonator

volume V acting as an acoustical spring and of the mass

of the resonator throat characterized by the opening

cross section S and the throat depth I. In resonance

condition and if the characteristic impedance of the

resonator matches that of the air, the ambient sound

field is deprived of a large amount of energy. To this

effect a damping material of a defined specific sound

impedance is placed in the resonator throat or in the

cavity volume.

mcL 1.2**l*

H

= ---- -

** 0.37 for U.S. system

l*1S

2

| +---R

H

H SR

2

ab

= ---------

Figure 7-48. Hole-area ratio of perforated panels with

round holes.

a

R

b