In an air$-$filled rectangular PEC waveguide with b $=5\mathrm{.}6896$ mm and a $=2\mathrm{.}8448$ mm$,$ the x$-$component of the TE mode is given by Ex $=2$ sin $(3$y b $)$ cos$(3\mathrm{.}285$ $1011$t $$ z$)$ V$/$m Find $($a$)$ the operating mode, $($b$)$ the phase constant $($c$)$ the intrinsic impedance $($d$)$ the group velocity.