energy relativistic Doppler shift Doppler shift
Fig. 6-1 (top). Consider a system of plane waves of light having frequency 



f


{\displaystyle f}

 traveling in direction 



ϕ


{\displaystyle \phi }

 relative to the x-axis of reference frame S. The frequency (and hence energy) of the waves as measured in frame S′ that is moving along the x-axis at velocity 



v


{\displaystyle v}

 is given by the relativistic Doppler shift formula which Einstein had developed in his 1905 paper on special relativity:
