The figure below shows the circular cross section of an infinitely long metallic waveguide with an infinitesimally thin, metallic baffle inserted into its otherwise hollow interior. The baffle has infinite length and a width equal to the radius R of the waveguide.
(a) Show that the baffle increases the lowest cutoff frequency for TM modes.

(b) Show that the baffle decreases the lowest cutoff frequency for TE modes.

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R