Civil Engineering Reference
In-Depth Information
3
Acoustic impedance at oblique
incidence in fluids. Substitution
of a fluid layer for a porous layer
3.1
Introduction
The dilatational plane waves studied previously have equiphase planes and equiamplitude
planes which are both perpendicular to the direction of propagation. These waves are
called homogeneous plane waves. They have been used to represent the acoustic field
in layered fluids having plane boundaries perpendicular to the direction of propagation.
Transmission and reflection at oblique incidence may be described by inhomogeneous
waves, with nonparallel equiphase and equiamplitude planes. A short description of these
waves is presented in this chapter, both in isotropic and in anisotropic fluids. Next,
these waves are used to calculate the surface impedance and the absorption coefficient of
both isotropic and anisotropic highly porous materials according to the laws of Delany
and Bazley (1970).
3.2
Inhomogeneous plane waves in isotropic fluids
In Chapter 2, waves propagating parallel to a coordinate axis have been considered. The
same plane waves can propagate in any direction defined by a unit vector
n
if the fluid
is isotropic. Let
n
1
,
n
2
and
n
3
be the three components of
n
. The wave propagating in
the direction
n
is then described by the following two equations:
p(x
1
,x
2
,x
3
,t)
=
A
exp[
j(
−
k
1
x
1
−
k
2
x
2
−
k
3
x
3
+
ωt)
]
(3.1)
A
n
Z
c
exp[
j(
υ
(x
1
,x
2
,x
3
,t)
=
−
k
1
x
1
−
k
2
x
2
−
k
3
x
3
+
ωt)
]
(3.2)
