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This paper aims to shed some more light on one of the best known phenomena inthe field of physics, the Doppler effect, in particular, on its classicalversion. Although, as mentioned, it is a phenomenon already described more than150 years ago, the general case, even considering constant velocities,continues to be the subject of very recent bibliographical works which eithershow it incompletely or start from a not entirely accurate description of it.Here, general expressions of both frequency shift and aberration are obtainedby geometrical description and, more interestingly, by describing the phase ofthe wave in the reference frame in which the propagating medium is at rest. Thecoherence between the two points of view permits to contrast the validity ofthe proposed results, and allows for a generalization of the resultingexpressions for any reference frame, even those where the propagating medium isnot still.

The classical Doppler effect revisited by the mathematical description of the phase function