###
Generalized Scattering Coefficients

Generalizing the scattering coefficients at a multi-tube intersection
(§C.12) by replacing the usual real tube wave impedance
by the complex generalized wave impedance

from Eq.

(

C.152), or, as a special case, the conical-section

wave impedance
from Eq.

(

C.151),
we obtain the junction-

pressure phasor [

436]

where

is the complex, frequency-dependent, incoming,
acoustic

admittance of the

th branch at the junction,

is
the corresponding outgoing acoustic admittance,

is the
incoming traveling

pressure-wave phasor in branch

,

is the outgoing wave, and

is the admittance of a load at
the junction, such as a coupling to another simulation. For
generality, the formula is given as it appears in the multivariable
case.

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