Civil Engineering Reference
In-Depth Information
7
Point source above rigid framed
porous layers
7.1
Introduction
Sound propagation in a plane layered structure is described in the simplest way with
plane waves, and the Kundt tube can be used to measure the reflection coefficient of a
plane surface having limited lateral dimensions. In the medium audible frequency range,
it is easy to build, with a pipe and a compression driver, a sound source which is a good
approximation of a monopole source. The monopole field reflected by a porous layer
can provide useful information about the porous structure if an adequate modelling of
reflection is performed. An exact model for the reflected field and several approximations
are presented.
7.2
Sommerfeld representation of the monopole field over
a plane reflecting surface
The Sommerfeld representation provides an exact integral representation of the reflected
field. The monopole pressure field
p
is created by an ideal unit point source S. The
pressure field
p
only depends on the distance
R
from the source S (Figure 7.1)
exp
(
−
jk
0
R)
R
p(R)
=
(7.1)
where
k
0
is the wave number in the free air. The spherical wave can be expended into
plane waves using a two-dimensional Fourier transform (Brekhovskikh and Godin 1992),
