Civil Engineering Reference
In-Depth Information
1000
800
600
Re Z
400
200
0
−
200
Im Z
−
400
−
600
−
800
−
1000
0
0.5
1
1.5
2
2.5
3
3.5
4
Frequency (kHz)
Figure 2.7
The impedance
Z
at normal incidence of a layer of fibrous material of
=
10 000 N m
−
4
s, calculated according
thickness
d
=
10 cm, of normal flow resistivity
σ
to the laws of Delany and Bazley.
Fibrous
air
layer
M
M
2
M
1
d
′
Figure 2.8
A layer of fibrous material with an air gap between the material and the
rigid wall.
represented in Figure 2.9, and the absorption coefficient for the material with and without
an air gap is shown in Figure 2.10.
The interesting effect of the air gap appears clearly in Figure 2.10. The air gap
increases significantly the absorption at low frequencies. This is explained by the fact
that sound absorption is mainly due to the viscous dissipation, related to the velocity of
air in the porous medium. When the material is bonded onto a hard wall, the particle
velocity at the wall is zero, and thus the absorption deteriorates rapidly at low frequen-
cies. When backed by an air gap, the particle velocity at the rear face of the material
oscillates and reaches a maximum at the quarter-wavelength of the lowest frequency of
interest, thus increasing the absorption. This is an alternative to an increase of the material
thickness.
