Acoustical impedance defined by wave-function solutions of the reduced Webster equation.
The electrical impedance was first defined by Heaviside in 1884, and the analogy of the acoustical impedance was made by Webster in 1919. However, it can be shown that Webster did not draw a full analogy with the electromagnetic potential, the potential energy per unit charge. This paper shows that the analogous "acoustical potential" the potential energy per unit displacement of fluid, corresponds to the wave function Psi of the reduced Webster equation, which is of Klein-Gordon form. The wave function is found to obey all of Dirichlet, Von Neumann, and mixed (Robins) boundary conditions, and the latter give rise to resonance phenomena that are not elucidated by Webster's analysis. It is shown that the exact Heaviside analogy yields a complete analytic account of the one-dimensional input impedance, that accounts for both plane- and dispersive-wave propagation both at the origin and throughout the duct.
Forbes
Barbara J
BJ
Phonologica, PO Box 43925, London NW2 1DJ, United Kingdom. forbes@phonologica.com