Derivation of Plank's Equation on Blackbody Radiation: Standing Waves Explained

[Pangolin]

In the derivation of plank's equation on blackbody radiation, the radiation within the cavity must form standing waves and thus each frequency has a certain number of possible modes.

However, I have no idea why the radiation has to form standing waves. Why does the electric field have to be zero?
I'll be grateful if anyone can enlighten me on this. Thanks!

 

[topsquark]

In the derivation of plank's equation on blackbody radiation, the radiation within the cavity must form standing waves and thus each frequency has a certain number of possible modes.

However, I have no idea why the radiation has to form standing waves. Why does the electric field have to be zero?
I'll be grateful if anyone can enlighten me on this. Thanks!

I believe that the argument is that the radiation in the cavity has reached a sort of equilibrium with respect to the material containing the cavity. If the radiation were not a form of standing wave then the material would be gaining or losing energy when the radiation interacted with it. This argument is necessary for the "perfect black-body" definition, else the black-body could be losing energy due to thermal absorption from the material bounding the cavity, and no such energy is supposed to escape.

-Dan