The concept of waveguides was introduced by Geddes in 1989. That paper showed how Webster's horn equation lacked a sufficient description of the wave propagation in the horn to be accurate in directivity simulations. The concept of a waveguide as a direct solution to the wave equation was shown to be capable of exact solution, free of plane-wave assumption of Webster's equation. The original paper did not perform a complete calculation of the exact solution and in fact contained errors which have been of concern to some readers. The purpose of the present paper is to revisit the waveguide discussion and to proceed with an exact calculation of the wave propagation in an oblate spheroidal waveguide. These calculations will clear up the questions raised regarding the original paper as well as showing some new results.
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