What is the relationship between the size of the waveguide and wavelength?

The correct answer highlights the direct relationship between the size of the waveguide and the wavelength. In electromagnetic theory, the dimensions of a waveguide are crucial for supporting the propagation of waves within it.

The fundamental principle is that for a waveguide to effectively propagate a wave, its dimensions must be comparable to or larger than the wavelength of the transmitted signal. Specifically, in a rectangular waveguide, the smallest dimension typically needs to be on the order of half the wavelength of the mode being transmitted. As the wavelength increases, the waveguide must also increase in size to maintain effective propagation of the signal.

This relationship allows waveguides to be designed specifically for certain frequency bands, where the size can be scaled accordingly to match the wavelengths involved. Consequently, a change in wavelength necessitates a corresponding change in waveguide dimensions to ensure the proper functioning of the waveguide system.