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I'll start with the second of your questions. Yes, light from very distant galaxies gets redshifted to such long wavelengths that there practically isn't any light to see. The lower limit on frequency is zero. Obviously. Technically one could say there is no signal at $0\,Hz$, but that still put a lower boundary on the frequency. Objects on the edge of our ...

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Treating the wire and rails as a "transmission line," one obtains the wavelength of a 50 cycles per sec wave as $\lambda = c/f$, = $300x10^6 / 50 = 6x10^6m.$ 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, ...

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My fluid mechanics is not strong, but a steep increase in the pressure from a beam that you are heading towards as you approach the speed of light does indeed happen. You can reason this from several perspectives. Suppose you measure a plane wave in one frame and find out that the electric and magnetic field are $E_0\,\cos(\omega_0\,t)\,\hat{X}$ and ...

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