Help with microwave oven standing waves problem

[strugglingstu]

Homework Statement

Hey guys, I have a homework problem in my electromagnetism class that's got me a little stumped. I'm supposed to measure the interior dimensions of my microwave oven and use that to calculate the 5 lowest frequencies at which I can sustain a mode in which I have standing waves. EDIT: I can assume that there is no metal "stirring" blade that modifies the propagation of waves exiting the waveguide.

I remember reading that in order to achieve standing waves the length of a cavity (in this case, my microwave oven's interior) must be an integer multiple of the wavelength or else the reflected waves will be out of phase and eventually cancel. I measured my microwave's cavity and its dimensions are h = .232m, w = .336m, d = .348m.

Homework Equations

λ = c/f
λ*n = h (or) w (or) d <-- May not be true, I came up with this.
Maxwell's Equations
Wave Equations
Boundary Conditions

The Attempt at a Solution

Now, I'm about to make some assumptions (which can be a dangerous thing, and I don't expect the correct answer to be this simple). If I assume that my waves are entering from the top of the cavity and only propagating straight down, then I can simply find the first 5 wavelengths that satisfy n*λ = h = .232m (for n=1,2,3,4,5). This gives me lengths of .232m, .116m, .0773m, .058m, and .0464m for respective frequencies of 1.29 GHz, 2.59 GHz, 3.88 GHz, 5.17 GHz, and 6.47 GHz.

The problem with this logic is that microwaves typically do enter the oven's cavity from a waveguide located above, but they are sent out in all directions by a metal stirring blade which disperses the waves in multiple directions. How can I go about incorporating that into my solution?

Am I on the right track? Can you guys offer some guidance?

 

[Redbelly98]

I remember reading that in order to achieve standing waves the length of a cavity (in this case, my microwave oven's interior) must be an integer multiple of the wavelength or else the reflected waves will be out of phase and eventually cancel.

That's almost right. But you need to consider the "round trip" length of a wave propagating back and forth along, for example, the interior height. A round trip is actually 2h.

I'm honestly not sure if width and depth are to be considered here (the whole issue of the stirring blade, I guess) and leave that part to your judgement -- or to anybody else in here.

Other than that, you're on the right track.

p.s. Welcome to PF.