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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.149), or, as a special case, the conical-section wave impedance
from Eq.(C.148),
we obtain the junction-pressure phasor [440]
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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