Handbook for Sound Engineers

Acoustics for Auditoriums and Concert Halls 183

7.3.4.4 Sound Absorbers

Sound absorbers can occur in the shape of surfaces,

built-in elements, pieces of furniture, or in the form of

unavoidable environmental conditions (e.g., air) as well

as arrangements conditioned by utilization of the room

(e.g. spectators, decorations). According to their prefer-

ential effect in a determined frequency range one distin-

guishes on principle between

• Absorbers in the low-frequency range between
  approximately 32 Hz and 250 Hz.


• Absorbers in the medium-frequency range between
  approximately 315 Hz and 1000 Hz.


• Absorbers in the high-frequency range between
  approximately 1250 Hz and 12 kHz.


• Broadband absorbers.

For acoustical characterization of a sound absorber
there serves its frequency-dependent sound absorption
coefficient D or the equivalent sound absorption area A.
For an area of size S one determines the equivalent
sound absorption area A as

(7-56)

The sound power Wi being incident on an area of size

S of a sound-absorbing material or a construction is

designated as sound intensity Ii, part of which is

reflected as sound intensity Ir, and the rest is absorbed

as sound intensity Iabs. The absorbed sound intensity

consists of the sound absorption by dissipation (trans-

formation of the sound intensity Ið in heat, internal

losses by friction at the microstructure or in coupled

resounding hollow spaces), and of the sound absorption

by transmission (transmission of the sound intensity IW

into the coupled room behind the sound absorber or into

adjacent structural elements).

(7-57)

With the sound reflection coefficient defined as

(7-58)

and the sound absorption coefficient D as

(7-59)

as a sum of the dissipation coefficient G

(7-60)

and the transmission coefficient

(7-61)

Eq. 7-57 becomes

(7-62)

The transmission coefficient W plays a role when

considering the sound insulation of structural compo-

nents. For nonmovable, monocoque, acoustically hard

material surfaces (e.g., walls, windows), it is, according

to Cremer,^48 possible to consider the frequency depen-

dence of the transmission coefficient as a low-pass

behavior which surpasses the given value up to a limit

frequency fW. With a negligible dissipation coefficient it

is furthermore possible to equate the transmission coeffi-

Figure 7-45. Schroeder diffusor with primitive root
structure.

Figure 7-46. Boundary Element Methods (BEM) based soft-
ware tool for calculating scattering coefficients.

A=DS

Ii Ir+= Iabs

= Ir++IG IW

U

U

Ir

Ii

= ---

D

IG+IW

Ii

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

Iabs

Ii

---------=

G

IG

Ii

--- -=

W

IW

Ii

--- -=

1 =UGW++

= UD+