Past exam of the symmetry and relativity course of the University of Oxford / 2017 / 3 / b / a

Take the wave along positive $x$, so $k_x=\omega /c$. A longitudinal boost $\mathbf{V}=(v_x,0,0)$ givesA receiver moving in the propagation direction measures a redshift. The same signed expression gives a blueshift when $v_x<0$. If the original wave propagates along negative $x$ instead, retain $k_x=-\omega /c$ in the general formula.