While reading the Wikipedia page of Ultraviolet Catastrophe, I came across how Rayleigh and Jeans applied the equipartition theorem. They told that each mode must have same energy. Now as the number of modes are greatest in small wavelengths or large frequency, energy radiated will be infinite.
What is mode actually? And why do the large frequencies have the most modes? Please help me explaining these.
I need a math-free explanation.
Best Answer
The "modes" in this case refer to the standing waves that can exist in a cavity. A very nice diagram / explanation is given at http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html
To summarize: if you consider a cavity of dimension $L$, the modes that fit inside the cavity have wave numbers $n_1$, $n_2$, $n_3$ such that
$$n_1^2 + n_2^2 + n_3^3 = \frac{4L^2}{\lambda^2}$$
It then goes on to show that the number of these modes (represented as dots on the surface of a sphere) increases as the radius of the sphere increases (which it does with the inverse of the wavelength).
See the link for all the details.