Civil Engineering Reference
In-Depth Information
This coefficient has the same interpretation as the absorption coefficient at normal
incidence.
3.6
Examples
In Chapter 2, the surface impedance and the absorption coefficient for a layer of fibrous
material with and without an air gap were calculated at normal incidence. Since fibrous
materials are not isotropic, the formalism which has been worked out in the present
chapter cannot be used for these materials. The sound propagation in porous foams with
a flow resistivity of about 10 000 N m
−
4
s or less can be described approximately by the
laws of Delany and Bazley. As these materials are generally not noticeably anisotropic,
the formalism previously worked out can be used.
The surface impedance of an isotropic porous material of porosity close to 1, of
flow resistivity
σ
equal to 10 000 N m
−
4
s, and of thickness
d
equal to 10 cm, has been
calculated for the two configurations indicated in Figure 3.6.
In the first configuration, the material is fixed to a rigid impervious wall. The front
face of the material is in contact with air. The angle of incidence is real and equal to
π
/4
radians. In the second configuration, there is an air gap of thickness
d
=
10 cm between
the porous material and the wall. The angle of incidence
θ
is the same in the air gap as
in the air in front of the porous material.
It follows from Equation (3.27) that, in both configurations, the component
k
3
of
k
in the porous material is
k
2
4
1
/
2
−
k
o
sin
2
π
k
3
=
(3.46)
where
k
o
and
k
are the wave number in air and in the porous material, respectively. The
wave number
k
is calculated by means of Equation (2.29). The surface impedance for the
first configuration is evaluated by Equation (3.39),
Z
c
being given by Equation (2.28).
In the case of the second configuration, Equation (3.36) may be used. The impedance
porous
layer
porous
layer
air
air
air
M
M
′
M
M
′
M
1
θ
X
3
θ
X
1
d
d
′
d
(1)
(2)
Figure 3.6
First configuration: the material is fixed to an impervious rigid wall. Second
configuration: there is a gap of air of thickness d
between the material and the rigid wall.
In both cases, the front face of the porous material is in contact with air.
