Help with microwave oven standing waves problem

In summary, the conversation is about a student seeking help with a homework problem involving measuring the dimensions of a microwave oven and using that information to calculate the lowest frequencies at which standing waves can be sustained. The student has made some assumptions about the waves entering the cavity and is looking for guidance on incorporating the role of the metal stirring blade into their solution. The main concept is that the length of the cavity must be an integer multiple of the wavelength for standing waves to occur.
  • #1
strugglingstu
1
0

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?
 
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  • #2
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.
 
  • #3


Hi there, it looks like you have a good understanding of the concept of standing waves and the relationship between cavity dimensions and wavelength. However, you are correct in assuming that the presence of a metal stirring blade will affect the propagation of waves in the microwave oven. To incorporate this into your solution, you can consider the blade as a boundary condition for the wave equation, which will affect the allowed wavelengths and frequencies for standing waves in the cavity. You may need to use more advanced mathematical techniques, such as solving the wave equation with boundary conditions, to find the correct frequencies for standing waves in this scenario. I would suggest consulting your textbook or seeking help from your professor or a tutor for guidance on how to approach this problem. Good luck!
 

1. What causes standing waves in microwave ovens?

Standing waves in microwave ovens are caused by the reflection of microwaves off the walls of the oven. This creates interference patterns that result in areas of high and low energy, leading to uneven heating of food.

2. How can I tell if my microwave oven has standing waves?

You can test for standing waves in your microwave oven by placing a microwave-safe plate with a layer of marshmallows or chocolate chips in the oven and running it for 30 seconds. If there are hot spots or areas where the food has not melted evenly, it is likely due to standing waves.

3. Is standing waves in microwave ovens dangerous?

While standing waves can lead to uneven heating of food, they are not considered dangerous. The microwaves used in ovens are not powerful enough to cause harm. However, it is important to properly maintain and use your microwave to prevent any potential risks.

4. How can I fix standing waves in my microwave oven?

If you are experiencing standing waves in your microwave oven, it is recommended to have it serviced by a professional. They can adjust the position of the waveguide or ensure that the oven's walls are properly sealed to prevent reflection of microwaves.

5. Can standing waves be prevented in microwave ovens?

While standing waves cannot be completely prevented, they can be reduced by properly positioning food in the center of the turntable and avoiding placing metal objects or containers with sharp edges in the oven. Regular maintenance and cleaning of the oven can also help prevent standing waves.

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