Abstract
A method for analyzing high-frequency signal propagation in rectilinear waveguides consisting of interconnected segments has been proposed [Ginsberg, POMA 19, 030104 (2013)]. The signal within each segment is represented as a series of modes that either propagate or evanesce in the forward and backward directions. The state variables are the modal amplitudes. Equations for these parameters are obtained by satisfying continuity and boundary conditions on pressure and axial particle velocity at preselected points on transitional cross-sections. This leads to a sequential evaluation of transfer functions for the modal amplitudes. The present work will examine the convergence and accuracy properties of the formulation by comparing its results to those obtained from a classical orthogonality analysis. The system consists of a pair of coaxial circular hard-walled cylinders axisymmetrically excited by a piston covering half the radius at one end, and the other end is rigidly closed. The frequency for the evaluation is slightly greater than the cutoff value for the sixth mode in the narrower segment. Aspects that are examined are computer code verification, metrics for comparing analyses, the influence of the number and placement of the collocation points, and the influence of evanescent modes.
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