Since the speed of light is same for everyone, then why does Doppler effect occurs?

because according to wave theory of light, light is made up of waves. A wave has a crest and trough since the speed of light is same, each crest & tough should also move at the same speed (because they make up a light) But in reality if a light source is moving towards us, it undergoes blueshift, which means each consecutive wave took less time to hit our eye or sensor, therefore each waves shrink together because of motion & viceversa in red shift. Doesn't that violate relativity? but i know they also have a theory on relativistic Doppler effect! What do you think?