Q$.1$ a$)$ Calculate the cut$-$off frequencies of the first two propagation mode for a WR$-62$waveguide with the dimensions: $\backslash ((15,8\backslash$times $7,9\backslash$mathrm$\{$~mm$\})\backslash )$

b$)$ Calculate the bandwidth for single$-$mode propagation.

c$)$ Calculate the phase and group velocities for this waveguide for $\backslash ($ f$=15\backslash$mathrm$\{$GHz$\}\backslash ).($The waveguide is filled by air.$)$