Civil Engineering Reference
In-Depth Information
e
Figure 4.10
A layer of porous material with identical parallel pores perpendicular to
the surface in a normal plane acoustic field. Arrows represent the trajectories of air
molecules.
M
2
M
1
Z
Figure 4.11
A simplified representation of the porous material of Figure 4.10.
Two impedances,
Z(M
2
)
in free air and
Z(M
1
)
in a pore, can be defined at the surface
Z(M
2
)
=
p(M
2
)/υ(M
2
),
Z(M
1
)
=
p(M
1
)/υ(M
1
)
(4.132)
related by
φZ(M
2
)
=
Z(M
1
)
(4.133)
The wave equation in a pore is
K
∂
2
υ
∂z
2
ρ
∂
2
υ
∂t
2
=
(4.134)
The bulk modulus
K
and density
ρ
are given by Eqs. (4.125) - (4.129). The charac-
teristic impedance
Z
c
and the complex wave number
k
in a pore can be calculated by
the equation
(Kρ)
1
/
2
,
ω(ρ/K)
1
/
2
Z
c
=
k
=
(4.135)
The impedance
Z(M
1
)
may be calculated by Equation (2.17)
Z(M
1
)
=−
jZ
c
cot g
kd
(4.136)
