Question regarding rectangular waveguide

Does anybody know how to find the dielectric constants of a waveguide, given the guide wavelength, operation frequency and the waveguide's dimensions.

In any medium where a dielectric is present, the effective wavelength is shorter than that in vacuum by a reverse square root of the real part of permittivity. It hold also for waveguides.

If you can measure the wavelength in a waveguide with a dielectric filling, then you can calculate the real part of its permittivity knowing the wavelength in the same waveguide without the dielectric.

I don't know exactly what "waveguide" is being discussed here But if its what I think it is, then the wave will be partially in vacuume, andd partially in the dielectric. So the effective permittivity will be somwehre between that of vacuum and of the material. So it's not clear to me that a simple wavelength measurement will allow one to calculate the relative permittivity.

Dave