The Doppler Frequency Shift Formula Derived by Directly Differentiating the Wave Speed Formula

In the relative motion system composed of the wave source and observer, the wave velocity formula has been extended and modified, directly treating the velocity in the wave velocity formula as a variable. Then, the relationship between the change in velocity and the change in frequency can be obtained through differentiation. By further attributing the change in velocity to the relative motion between the wave source and observer, the Doppler shift formula can be derived. Compared with all existing methods for deriving Doppler formulas, the method proposed in this paper that performs differential analysis on the extended and modified wave velocity formula seems to be the simplest.