Question

Your microwave oven produces waves of frequency 2.450 Ghz. Somewhere inside there is a resonant cavity.  ...

Your microwave oven produces waves of frequency 2.450 Ghz. Somewhere inside there is a resonant cavity.   (A) Design the cavity with smallest possible surface area that will resonate at this frequency, either in the form of a cubical box or a circular cylinder.   (Exactly solving this involves solving a transcendental equation.   But a solution that is within 10% isn’t very hard).
(B) The microwaves get from the generator to the interior of the oven through a waveguide.   How large should it be for the cutoff frequency to be less than 2.45 Ghz?

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