A cavity resonator is a region surrounded entirely by conducting walls. Consider a cubic cavity resonator of side and let

Each component E_0i (x,y,z) where i = x,y,z must satisfy the Helmholtz wave equation :

1- Use the boundary conditions on the tangential part of E₀ at the conducting surfaces to show that:

2- Find k_x, k_y, k_z

3- Find  in terms of a² and your values of k from (2).