# Measuring the speed of light with chocolate and a microwave oven

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#### Meir Achuz

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It could also be used to measure the frequency of the microwave, which is not as well known as c.

#### sophiecentaur

Gold Member
The method, of course, uses the fact that someone else measured the frequency of the microwave radiation. It's just an alternative way of measuring / knowing time.

#### Jilang

I think that's splendid. What a great way to engage all chocolate lovers in the experimental method!

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#### AlephZero

Homework Helper
from the OP's link:
Edit: when I made this measurement I forgot that I was measuring peaks of a standing wave which are half the wavelength of the microwave. So really, you should find the distance between the soft spots and multiply by 2 to get the wavelength. Thanks, Lord Axil. Somehow I must have missed a soft spot when measuring, which automatically corrected this factor of two.
More likely, he didn't realize his method was wrong in principle, but he got lucky and two errors canceled out.

The big conceptual error is assuming that the EM waves are traveling in a horizontal plane, so you can assume the distance between the spots = the wavelength (or half a wavelength, if you don't like the answer you got the first time!). The only "waves" that will produce heat spots in a fixed location are standing waves, and in a rectangular box like a typical microwave the standing waves are three dimensional. They can be very complicated - the wave can reflect off the walls, roof and floor of the box and make several "orbits" around the box before it repeats. What you are measuring is only a slice cut through that 3-D wave pattern. If you want to explore this further, it might be interesting to repeat the experiment at several different heights from the floor to the top of the oven, and compare the different patterns you get. Make sure you measure the positions of the spots relative to the sides of the oven, so you can "stack up" the different layers correctly.

The "real" wavelength inside the oven is something like $\sqrt{kx^2 + ly^2 + mz^2}/n$, where x y and z are the width, height, and depth of the oven, and k,l,m,and n are four unknown integers. If you knew the values of k,l,m, and n, you could relate that to the pattern of spots you measured. The only problem is that you don't know what the integers were.

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#### thegreenlaser

from the OP's link:

More likely, he didn't realize his method was wrong in principle, but he got lucky and two errors canceled out.

The big conceptual error is assuming that the EM waves are traveling in a horizontal plane, so you can assume the distance between the spots = the wavelength (or half a wavelength 1/2, if you don't like the answer you got the first time!). The only "waves" that will produce heat spots in a fixed location are standing waves, and in a rectangular box like a typical microwave the standing waves are three dimensional. They can be very complicated - the wave can reflect off the walls, roof and floor of the box and make several "orbits" around the box before it repeats. What you are measuring is only a slice cut through that 3-D wave pattern. If you want to explore this further, it might be interesting to repeat the experiment at several different heights from the floor to the top of the oven, and compare the different patterns you get.

The "real" wavelength inside the oven is something like ##\sqrt{kx^2 + ly^2 + mz^2}/n, where x y and z are the width, height, and depth of the oven, and k,l,m,and n are four unknown integers. If you knew the values of k,l,m, and n, you could relate that to the pattern of spots you measured. The only problem is that you don't know what the integers were.
That's pretty much the argument in the link I posted (he has some nice pictures to go along with it). Basically, it seems like this experiment only "works" because there will usually happen to be some hot spots whose distance apart is at least in the right order of magnitude, and then you can increase your precision either by hand-wavy measurements or by adding in factors of two as needed. :D

(I'll admit, though, I was kind of disappointed when I found out this experiment doesn't really work... it was one of my favourites in high school.)

#### Naty1

posts 6,7 good insights....

I almost didn't post the link wondering about such....I was thinking reflections but wondered if there was some way manufacturers suppress them...then decided against that since it would seem to dimish delivered power [efficiency]....already not great....and it seems there are metal interior walls so anything outside would seem to have minimal effect.

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