Blackbodies and Maxwell's Whole Number Wavelength Theory

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Apophilius
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I've been reading The Elegant Universe by Brian Greene and everything has rolled along smoothly until just recently. He writes:

Brian Greene said:
It turns out that when Maxwell's electromagnetic theory is applied to the radiation in an oven it shows that the waves generated by the hot walls must have a whole number of peaks and troughs that fit perfectly between opposite surfaces.

Furthermore:

Brian Greene said:
Each of the allowed waves--regardless of wavelength--carries the same amount of energy

So here's my question. How does the ideal blackbody (which I assume the oven to be in this case) magically know what wavelength to emit to fit perfectly between the sides of an oven? Is it a property of blackbodies, or have I simply missed something here?
 
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It's like the vibrations of a drumhead or of an organ pipe. Only the resonant waves that exactly fit within the length of the pipe will be found, because they're the only ones that can persist. Waves with other wavelengths die out.
Each of the allowed waves--regardless of wavelength--carries the same amount of energy
Bear in mind that Greene's describing a paradox here. He immediately adds that this classical version of blackbody radiation leads to infinite total energy, and is therefore obviously wrong, and for that reason needs to be replaced by the quantum version.
 
I hate to be a pain, but can you elaborate more on how exactly they die out?

And I had thought that as frequency reaches a certain threshold, the minimum possible energy exceeds that allowed for each wave and therefore they cannot exist. So the statement isn't entirely false, is it? All the waves that can exist have the same amount of energy.
 
Ask yourself, how would you envision such a wavelength in a piece of string? For the second part of your last question, I'm not sure what you mean, but I think you have a wrong idea about the energy carried by a wave, in terms of wavelength vs. amplitude.
 
So if the resonant frequencies are the only ones that exist within the oven, the waves that are detected are standing. Do resonant wave mechanics apply just the same then for the light bouncing around?

And what I said was that blackbodies emit energy, with equal distribution of energy to all frequencies of light within the possible range of frequencies. When you get a frequency with minimum energy that exceeds the energy threshold allowed for frequencies, it doesn't exist. Is this a correct statement? If not, how is it incorrect?
 
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