A resonant cavity of copper consists of a hollow, right circular cylinder of inner radius R and length L, with flat end faces.

(a) Determine the resonant frequencies of the cavity for all types of waves. With (1/√με R) as a unit of frequency, plot the lowest four resonant frequencies of each type as a function of R/L for 0 < R/L < 2. Does the same mode have the lowest frequency for all R/L?

(b) If R = 2 cm, L = 3 cm, and the cavity is made of pure copper, what is the numerical value of Q for the lowest resonant mode?