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Is there a maximum frequency that an electromagnetic wave can support?

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No. There is an approximate limit to the wavelengths (spectrum) emitted by an object of a given temperature: in fact, before quantum mechanics, there was a problem called the "UV catastrophe" where calculations of the spectrum suggested there should be infinite power in the shortest wavelengths; QM could explain away this problem, and it was one of the early triumphs of the theory.

But in principle there is no limit (that I know of) on the energy of an individual photon - and therefore, no upper limit on the frequency.

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Yes(at least measurably). According to generalized uncertainty principle, the Planck length(1.616199e-35m)is the the shortest measurable length(within a factor of 10). So that can be the shortest wavelength possible. Which gives maximum frequency to be 6.187356e34 Hz. Plank length - Wikipedia

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