Bingo the Einsteiniano: Why not? The same formula for the frequency shift, f'=f(1+v/c), will be obtained. Wait wait... "it is the effective velocity that changes"... No! Help! Help! Divine Einstein! Yes we all believe in relativity, relativity, relativity! The effective velocity of light never changes! Of sound - yes, of light - never! Divine Albert said so!
Question: For sound, the effective velocity changes and "leads to an apparent change in the frequency". For light, the effective velocity does not change but then what "leads to an apparent change in the frequency"?
Bingo the Einsteiniano: It is the wavelength that changes and leads to an apparent change in the frequency of the light.
Question: So the motion of the obsever cannot change the wavelength of sound but can change the wavelength of light?
Bingo the Einsteiniano: I think the motion of the observer changes the wavelength of both sound and light, in the following way: