Similarity of waves in dispersive media

Abstract

In a previous letter, D.A.Gurnett [1995] discussed the remarkable fact that atmospheric whistlers propagate under the same emission cone relative to the earth's magnetic field as bow waves do with respect to the ship's velocity—namely under 19°28′. The present contribution is a comment on Gurnett's letter and considers a prerequisite for the occurence of the similarity of both phenomena: the independence of the wave features of parameters such as the ship's speed or the earth's magnetic field. It is found that media with dispersion relations of the form ω ∼ kα show such independence; a more general solution is also given.