Derivation of general Doppler effect equations

In this paper, we will derive the general equations for Doppler effect. It will be proved that regardless of the nature of the emitted waves and the medium through which the waves propagate the formula always has the same form and is identical to the general Doppler effect formula for sound. We will also show that Doppler effect can be used to establish a relationship between the local time of the source and the local time of the receiver. In addition, some new characteristics of the Doppler effect have been presented that have not been discussed in the literature so far.