A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensi...

A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a = 5 cm and b = 3 cm. If the x-component of its electric field is given by

determine:

(a) the mode number,

(b) εr of the material in the guide,

(c) the cutoff frequency, and

(d) the expression for Hy