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.173), or, as a special case, the conical-section wave impedance from Eq.(C.172), 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.