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I'm reading articles about black body radiation and why classical mechanics fails to explain it. My question is:

Why do EM waves have to be standing wave in a cavity?

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  • $\begingroup$ Standing waves do not transfer energy, and the definition of a black body includes thermal equilibrium, i.e. no heat transfer. $\endgroup$ – auxsvr Jun 16 '14 at 7:36
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I'm reading articles about black body radiation and why classical mechanics fails to explain it.

More correctly, people could not explain it with classical physics (pre 20-th century physics). Nobody seriously thought that classical mechanics was sufficient even then - radiation is described by electromagnetic theory, not mechanics.

Why do EM waves have to be standing wave in a cavity?

They do not have to be. Standing waves are only special kind of waves that can occur in perfectly reflecting cavity. This is because the component of electric field in the walls along these walls is zero for perfect conductor.

We talk about standing waves because 1) we consider perfectly reflecting cavity 2) because all possible states of the EM radiation (even those that are not standing waves) can be expressed as sum of such standing waves.

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