A one‐to‐one correspondence is demonstrated for Doppler shifted frequencies measured in different inertial reference frames. This result is reconciled with frequency splitting encountered in the complex Doppler effect. The analysis emphasizes the concept that it is not always sufficient to describe the Doppler effect for plane waves in homogeneous, isotropic, dispersive media by using only the conventional frequency equation ω=γ (ω′+v⋅k′). These ideas are illustrated in detail for the case of the cold plasma where the extra Doppler frequencies are given specific physical interpretations.