Today in my electro-magnetics class, we were told that the cut-off frequencies of TE and TM waves on a co-axial cable are different. As far as I understand, it says that if there is an electric field with one frequency projected on it and if we know that the problem can be simplified if we see it as a combination of one TE and one TM wave, as the wave travels inside the medium, it is treated differently because of two different cut-off frequencies. The cut-off frequency I am referring here is the frequency below which the propagation constant is imaginary and above which the propagation constant is real. Imaginary propagation constant shows oscillating behavior. What is the significance of two separate cut-off frequencies for TE and TM, because we can visualize one wave as a combination of both? When I asked this, I got a good response, but I didn't get it properly. The response says that the properties of medium and waves are different and shouldn't be confused with one another. It comes down to the difference between phase and group velocities. What is the use case of two separate cut-off frequencies?