The resonant modes of a microwave oven

This project must be done by individuals.

In this class, we looked at electromagnetic waves bouncing around inside a rectangular box. If one knows the dimensions of the box, one can figure out the frequencies of the normal modes which will resonate inside the box.

If one sends waves with these resonant frequencies into the box, they will interfere constructively with other waves already inside the box. One can build up high energy densities using waves of these special frequencies, which might cook food placed inside the oven.

Your job is to figure out the resonant frequencies of the waves inside an ordinary microwave oven. Here's how:

measure the dimensions of the interior of the oven
write a general equation for the frequencies of the normal modes of this oven. Your expression should have factors of the three mode indices, n_x, n_y, n_z.
assume that the magnetron inside the oven produces waves which cover the range from 2400 to 2500 MHz; call this the "permitted range."
find as many combinations of the modes as you can which will yield resonant frequencies which lie within the permitted range
list all the combinations you found, together with the frequency of each combination

You might find the article by Hauck mentioned in the "For more information" section of that lecture a good source of background information.

Hand in a sheet of paper, showing all your work. Provide photographs of your oven, either in hardcopy or electronically. A small portion of your score will depend upon the number of combinations you can find. The larger your list, the higher your score.