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

 

[denian]

The concept of standing waves is crucial in understanding blackbody radiation and is based on the principles of classical physics. When electromagnetic radiation is confined within a cavity, it can only exist at certain discrete frequencies, known as modes. This is because the radiation must satisfy the boundary conditions of the cavity, meaning that the electric field must be zero at the walls of the cavity.

This requirement for the electric field to be zero at the walls of the cavity leads to the formation of standing waves, where the electric field oscillates between positive and negative values at fixed points within the cavity. This is similar to the behavior of a guitar string, where the ends are fixed and the string can only vibrate at certain frequencies, known as harmonics.

The concept of standing waves is important in the derivation of Plank's equation because it helps to explain the distribution of energy within the cavity and the relationship between frequency and energy. It also helps to explain why the radiation within the cavity has a discrete, rather than continuous, distribution of frequencies.

In summary, the requirement for the electric field to be zero at the walls of the cavity is a fundamental principle in the derivation of Plank's equation on blackbody radiation. It is based on the principles of classical physics and plays a crucial role in understanding the behavior of electromagnetic radiation within a confined space.