Handbook for Sound Engineers

184 Chapter 7

cient W numerically to the sound absorption coefficient D.

7.3.4.4.1 Sound Absorption Through Porous Materials

The effect of sound absorption is based essentially on
the transformation of sound energy in thermal energy by
air particles moving in open, narrow, and deep pores.
Closed pores like those existing in foamed materials
used for thermal insulation are unsuited for sound insu-
lation. For characterizing the materials the so-called
porosity V is used. This represents the ratio between
open air volume Vair existing in the pores and the overall
volume Vtot of the material

(7-63)

With a porosity of V= 0.125, it is possible for high
frequencies to obtain a maximum sound absorption
coefficient of only D= 0.4, and with V= 0.25 of
D= 0.65. Materials with a porosity of Vt0.5 enable a
maximum sound absorption coefficient of at least 0.9.
Usual mineral, organic, and naturally growing fibrous
insulating materials feature porosities of between 0.9
and 1.0 and are thus very well suited for sound absorp-
tion purposes in the medium- and high-frequency
ranges.^29
Apart from porosity it is also the structure coefficient
s and the flow resistance ; which influence the sound
absorbing capacity of materials. The structure coeffi-
cient s can be calculated from the ratio between the total
air volume Vair contained in the pores and the effective
porous volume Vw

(7-64)

The insulating materials most frequently used in
practice have structure factors of between 1 and 2—i.e.,
either the total porous volume is involved in sound
transmission or the dead volume equals the effective
volume. Materials with a structure factor of the order of
ten show a sound absorption coefficient of maximally
0.8 for high frequencies.^8
The flow resistance exerts an essentially higher
influence on sound absorption by porous materials than
the structure factor and the porosity. With equal
porosity, for instance, narrow partial volumes offer a
higher resistance to particle movement than wide ones.
This is why the specific flow resistance Rs is defined as
the ratio of the pressure difference before and behind

the material with regard to the speed of the air flowing

through the material vair

(7-65)

where,

Rs is the specific flow resistance in Pa s/m (lb s/ft^3 ),

' p is the pressure difference in Pa (lb/ft^2 ),

vair is the velocity of the passing air in m/s (ft/s).

With increasing material thickness the specific flow

resistance in the direction of flow increases as well.

7.3.4.4.2 Sound Absorption by Panel Resonances

Thin panels or foils (vibrating mass) can be arranged at

a defined distance in front of a rigid wall so that the

withdrawal of energy from the sound field in the region

of the resonance frequency of this spring-mass vibrating

system makes the system act as a sound absorber. The

spring action is produced herewith by the rigidity of the

air cushion and the flexural rigidity of the vibrating

panel. The attenuation depends essentially on the loss

factor of the panel material, but also on friction losses at

the points of fixation.^43 The schematic diagram is shown

in Fig. 7-47, where dL is the thickness of the air cushion

and mc the area-related mass of the vibrating panel.

The resonance frequency of the vibrating panel

mounted in front of a rigid wall with attenuated air space

and lateral coffering is calculated approximately as

(7-66)

where,

fR is in Hz,

is in kg/m^2 (lb/ft^2 ),

dL is in m (ft).

In practical design one should moreover take into

account the following:

• The loss factor of the vibrating panel should be as
  high as possible.^43

V

Vair

Vtot

= ---------

s

Vair

Vw

= ---------

Figure 7-47. General structure of a panel resonator.

Rs 'p

vair

= --------

fR^60

*

mcdL

|----------------

* 73 in U.S. units

mc

m’

dL