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EM does not have the property of frequency, it has the property of duty cycle. Light does not transverse during propagation, like a media wave.EM is intermittent duration, not frequency. That duration is mirrored and doubled, when absorbed. And that duration, depends, on the absorber's relative velocity.The duration and velocity of propagation, relative to the emitter, is constant. This is due to the fact that the dynamic of emission is instant. And that instant has the property of a static point source in space. No matter the velocity of emitter. But, But...the duration of absorption can vary, depending on the absorber's relative velocity to emitter. Absorption takes time. Emission takes no time.
Emission is just a change in direction, not a change in speed or growth. The field and speed is already there. That's why it is instant.