Civil Engineering Reference
In-Depth Information
where
ρ
o
and
c
o
are the density of air and the speed of sound in air (see Section 2.2.2),
and
X
is a dimensionless parameter equal to
X
=
ρ
o
f/σ
(2.30)
f
being the frequency related to
ω
by
ω
2
πf
.
Delany and Bazley suggest the following boundary for the validity of their laws in
terms of boundaries of
X
, as follows:
=
0
.
01
<X<
1
.
0
(2.31)
It may not be expected that single relations provide a perfect prediction of acoustic
behaviour of all the porous materials in the frequency range defined by Equation (2.31).
More elaborate models will be studied in Chapter 5. Nevertheless, the laws of Delany
and Bazley are widely used and can provide reasonable orders of magnitude for
Z
c
and
k
. With fibrous materials which are anisotropic, as indicated previously, the flow
resistivity must be measured in the direction of propagation for waves travelling in either
the normal or the planar direction. The case of oblique incidence is more complicated
and is considered in Chapter 3. It should be pointed out that after the work by Delany
and Bazley, several authors suggested slightly different empirical expressions of
k
and
Z
c
for specific frequency ranges and for different materials (Mechel 1976, Dunn and
Davern 1986, Miki 1990).
2.6
Examples
As a first example, the impedance at the surface of a layer of fibrous material of thickness
d
equal to 10 cm, and of normal flow resistivity equal to 10 000 Nm
−
4
s, fixed on a rigid
impervious wall (Figure 2.6), has been calculated with the use of Equations (2.17), (2.28)
and (2.29).
The real and the imaginary parts of the impedance
Z
are shown in Figure 2.7.
As a second example, the impedance of the same layer of fibrous material with an
air gap of thickness
d
equal to 10 cm (Figure 2.8) has been calculated.
The general method of calculating
Z(M)
is given in Section 2.3.3. In the example
considered, Equation (2.16) can be used,
Z(M
1
)
being the impedance of the air gap.
The values of
Z
o
and
c
o
are used to calculate
Z(M
1
)
with Equation (2.17). Expressions
(2.28) and (2.29) for
Z
c
and
k
for the fibrous material have been used. The impedance is
M
d
Figure 2.6
A layer of porous material fixed on a rigid impervious wall.
