Use the results of Prob. 7-3, and show that the fractional change in resonance due to metal walls is
where coo is the resonant frequency of the cavity with perfectly conducting walls.
Prob. 7-3
Use the results of Prob. 7-2 and the approximations
To show that
Use the relationship
And show that the
formula gives
Note that the 'formula for Q is identical to the one that we have been using if
where ri is the intrinsic impedance of the conducting walls.
Prob. 7-2
Consider the perturbation of a cavity (say Fig. 7-1a) from one having perfectly conducting walls to one having a wall impedance Z, defined by
1 Morse and Rubenstein, The Diffraction of Waves by Ribbons and Slits, Phys. Rev., vol. 54, no. 11, pp. 895-898, December, 1938. 2 J. W. Miles, On the Diffraction of an Electromagnetic Wave through a Plane Screen, J. Appl. Pity., vol. 20, no. 8, pp. 760-770, August, 1949.
at the walls. Show that the exact perturbational formula is
where the subscript 0 denotes unperturbed quantities. Note that coo is real but w is complex if Z has a real part.
