  We prove the unique solvability, passivity/conservativity and some regularity
results of two mathematical models for acoustic wave propagation in curved,
variable diameter tubular structures of finite length. The first of the models
is the generalised Webster's model that includes dissipation and curvature of
the 1D waveguide. The second model is the scattering passive, boundary
controlled wave equation on 3D waveguides. The two models are treated in an
unified fashion so that the results on the wave equation reduce to the
corresponding results of approximating Webster's model at the limit of
vanishing waveguide intersection.
