For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencies for $$T{E_{10}}$$ mode and $$T{E_{20}}$$ mode. If a $$ = \sqrt 5 \,cm$$, the value of b (in cm) is

The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is $${H_Z} = 3\,\,\cos \,\,(2.094\,\, \times \,\,{10^2}x)\,\,\,\cos \,(2.618\,\, \times \,\,{10^2}y)$$
$$\cos \,\,(6.283\,\, \times \,\,{10^{10}}t\, - \beta \,z)$$
The phase velocity $${V_p}$$ of the wave inside the waveguide satisfies

A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in $$T{E_{11}}$$ mode. The minimum operating frequency is

An air-filled rectangular waveguide has inner dimensions of $$3\,cm\,\, \times \,\,2\,\,cm\,$$. The wave impedance of the $$T{E_{20}}$$ mode of propagation in the waveguide at a frequency of 30 GHz is (free space impedance $$\,{\eta _0} = \,377\,\,\Omega $$)