# Doppler-shift of AC-electricity

A tram is powered by overhead wire, the wire has alternating voltage of 1000 V RMS, the frequency of the alternating voltage is 50 Hz. The rails are the other wire.

The tram is moving at speed 100 m/s away from the place where the overhead wire and the rails are connected to the electric grid.

Is the frequency of the electricity Doppler-shifted in the tram frame? Is the energy of the electricity reduced proportionally to the reduction of the frequency of the electricity?

• In reality, the electrons in the power wire are just "wiggling" back and forth around fixed positions, due to an electric field that runs through the wire at practically the speed of light. The Doppler effect probably doesn't apply in the way that you think it does. May 28, 2021 at 23:40

Treating the wire and rails as a "transmission line," one obtains the wavelength of a 50 cycles per sec wave as $$\lambda = c/f$$, = $$300×10^6 / 50 = 6×10^6m.$$
A "peak" detector on the tram detects the start of the wave and at the end of 1/50 of a second, it would have detected the end of the wave if it had not moved. However, since it is moving at 100m/s, at the end of 1/50 sec, the detector will move 100m/s × 1/50 sec = 2m. So the wavelength as measured on the tram, would be $$6.000002×10^6$$m. This gives a frequency of 49.999983 cycles per second, so the frequency is Doppler-shifted by 0.000017 cps. For the second question, assuming that the load is purely resistive (power factor = 1), the shift in frequency would have no effect on the energy being delivered.