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How can we prove that radio waves are sine waves? What makes them sine?

Answer:

Fourier says that only a sine wave has no harmonic content. The math works out that if you have any wave shape other than a sign wave, you can break it down into a group of sine waves of different harmonic frequency, phase, and amplitude. All those harmonics go to zero when the wave shape is a pure sine. We can tell that radio waves behave like a sine, you can run them through a narrowband filter, and no energy is lost. Maxwell's equations predict propagation and fields based on a sine wave, and anything other than that propagates as if it is multiple frequencies, which do not propagate energy as well. So mathematically, radio waves work as they measure to work only if you assume they are sine waves.

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