Problem 9.38 Consider the resonant cavity produced by closing off the two ends of a rect- angular wave guide, at z = 0 and at z = d, making a perfectly conducting empty box. Show that the resonant frequencies for both TE and TM modes are given by %3D w1mn = c7 / (1/d)² + (m/a)² + (n/b)², (9.204) for integers 1, m, and n. Find the associated electric and magnetic fields.

Problem 9.38 Consider the resonant cavity produced by closing off the two ends of a rect- angular wave guide, at z = 0 and at z = d, making a perfectly conducting empty box. Show that the resonant frequencies for both TE and TM modes are given by %3D w1mn = c7 / (1/d)² + (m/a)² + (n/b)², (9.204) for integers 1, m, and n. Find the associated electric and magnetic fields.