Parametric Solution of the Dispersion Relation for Guided Sound Propagation in Shallow Water

The normal-mode dispersion relation for guided propagation in a liquid layer lying above an infinitely deep liquid bottom appears as a transcendental equation relating the angular frequency ω and the horizontal wavenumber k in Perkeris' classic solution. It is shown in this paper that this transcendental equation may be solved exactly in a parametric form for any given normal mode. Equations are derived and discussed. They give frequency, phase velocity, and group velocity in terms of a single parameter μ and mode number n.