Recall that, in a parallel-plate waveguide, any mode that is below cutoff (f < fc) will not propagate but instead be attenuated in the z direction. This means that a properly designed section of waveguide may be used as a filter to select only lower-order modes while attenuating all the higher-order modes. Assume that a section of a parallel-plate air-filled waveguide with a plate separation of 7.11 mm is to be used at 15 GHz as a filter. The waveguide should attenuate all of the modes except the TEM mode as it propagates along the guide. Find the minimum length of waveguide needed to attenuate all higher-order modes (m