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The Doppler effect: a unified approach for sound and light waves

A derivation of the Doppler effect is presented where the analysis of the Doppler shift for sound is the same as for electromagnetic waves (in vacuum). Furthermore, for sound waves the treatment is the same no matter whether only the sounce (S) is moving (with respect to the medium), or only the observer (O), or both S and O. The analysis shows clearly that the basic cause of the Doppler shift is the relative velocity between S and O in all cases, and not just for electromagnetic waves (where individual velocities of S and O are not even definable). The difference in the expressions for the Doppler shift in different cases is due to other factors which are easy to understand.