Einsteinians teach that the moving light source, just like the moving sound source, emits a changed wavelength:
http://phys.org/news/2016-03-nonlinear-rotational-doppler-effect.html
"The acoustic Doppler effect can be experienced day in the real world every: An ambulance siren sounds sharper closer to the emergency vehicle; when the vehicle pulls away, the siren sound descends. This is due to the change of wavelength of the sound waves, which are compressed or stretched during the movement of the sound source, thus changing its pitch. The effect applies to all kinds of waves, including light waves. Similarly, as a star moves away from Earth, its emitted light wave is stretched, creating the so-called red-shift, i.e. a longer wavelength of light."
True for sound waves, false for light waves - the wavelength emitted by the moving light source is the same as the wavelength emitted by the stationary source:
http://newt.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htm
"In our animation, Zoe turns on the headlights of her space ship. She measures the speed of light from her headlights as c with respect to her."
That is, moving Zoe measures the speed of the light to be c, the frequency to be f, and the wavelength to be λ=c/f, just as stationary Zoe.
Conclusion: The moving light source does not emit shorter/longer wavelength. Rather, it emits faster/slower light. If the source starts moving towards the stationary observer with speed v, the speed of the light relative to the observer shifts from c to c'=c+v, as predicted by Newton's emission theory of light and in violation of Einstein's relativity. Accordingly, the frequency measured by the observer shifts from f=c/λ to f'=c'/λ, where λ is the wavelength and f is the frequency measured when the source is stationary. Exactly the same shifts, from c to c'=c+v and from f=c/λ to f'=(c+v)/λ, take place when the light source is permanently stationary but the observer starts moving towards the source with speed v:
http://www.hep.man.ac.uk/u/roger/PHYS10302/lecture18.pdf
"The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. (...) Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/λ waves pass a fixed point. A moving point adds another vt/λ. So f'=(c+v)/λ."
http://rockpile.phys.virginia.edu/mod04/mod34.pdf
"Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) [=(c+v)/λ] ... There are relativistic corrections, but these are negligible here."
Pentcho Valev