Define the
reflection coefficient of the
scattering junction as
Then we get the following
scattering relations in terms of
for
pressure waves:
Signal flow graphs for
pressure and
velocity are
given in Fig.
C.16.
It is a simple exercise to verify that
signal power is conserved by
checking that
.
(Leftgoing power is negated to account for its opposite
directionoftravel.)
So far we have only considered a plane wave incident on the left of
the junction. Consider now a plane wave incident from the right. For
that wave, the
impedance steps from
to
, so the reflection
coefficient it ``sees'' is
. By superposition, the signal flow
graph for plane waves incident from either side is given by
Fig.
C.17. Note that the
transmission coefficient is
one plus the reflection coefficient in either direction. This signal
flow graph is often called the ``KellyLochbaum'' scattering junction
[
297].
Figure C.17:
Signal flow graph for plane waves
incident on either the left or right of an impedance discontinuity.
Also shown are delay lines corresponding to sampled traveling
planewave components propagating on either side of the scattering
junction.

There are some simple special cases:

(e.g., rigid wall reflection)

(e.g., openended tube)

(no reflection)
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