### 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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