In doppler effect derivation why are the considerations for source moving different from that of observer moving?

Question

I've looked through the derivation of doppler effect in 2 cases ( source moving and observer moving).. Why can't we solve all the doppler effect problems in frame of observer and assume it is at rest?

Answer 1

If the waves are light waves then we can. But if the waves are sound waves, then there is a preferred reference frame in which the speed of sound is isotropic. Yours is a relativistic argument, and the principle of relativity does not apply to sound waves: there is a preferred frame of reference.