Measuring the Speed of Light...With a Microwave
Today in our weekly staff meeting for the Physics 140 Discovery Room, we tried an experiment to measure the speed of light using a microwave oven. We had been hoping to use this as one of the demos for the week, but we got rather poor results. Specifically, we measured the speed of light at about twice what it should be. This experiment has been done successfully before by others, see here for one example, but since our attempt failed we were all sent home to think about where our error was.
We used the fax paper method since it would be the cheapest and make the least mess. (Like we really wanted 600 students handling chocolate bars or eggs in there all week.) Anyway, here's what you need:
where c is the speed of light (which we're trying to get), f is the frequency of the microwave and lambda is the wavelength. Remember that microwaves are electromagnetic waves, just like light, and so they always travel at the speed of light.
So how do we measure the wavelength? Well, the way that a microwave cooks food is by setting up a standing wave inside the oven. Basically, microwaves are created by a device called a magnetron and shot into the main chamber. Then the waves reflect off of the metal walls and screen covering the door. This bouncing around sets up a well defined pattern of waves, called a standing wave. In one dimension, a standing wave just looks like a sine function,
In some places, the amplitude of the wave is large, meaning the electric field part of the wave is oscillating up and down at full strength, and in other places the amplitude is zero. The food in the microwave is cooked because the changing electric field forces the water molecules in the food to flip back and forth with the oscillation, heating the food. Conversely, the areas where there is no oscillation don't get heated. This is why your microwave rotates the food as it cooks, so that no part of the food is stuck in a place where it won't be cooked. The movie above shows one wavelength of a wave, the wavelength is the minimum distance it takes for the wave to repeat itself. Notice that the distance between the two peaks is half of a wavelength.
Our method for measuring the wavelength was to take some fax paper, which changes color from white to black when heated, and lay it over a moist paper towel on top of an upside down pyrex dish, like so
The only difference between what we did at the meeting and how I did it at home was that I made sure to press gently on the fax paper so that it was uniformly moist before starting. Then I just ran the microwave for about 15 seconds. The microwave heats the water and causes the fax paper to turn black. The idea is that we should be able to see a pattern of black spots where the microwaves have the highest amplitudes and that the distance between two spots will be half of the wavelength of the microwaves in the oven.
My first try produced this:
Two splotches, six centimeters apart. Which means that the wavelegth of the waves in the microwave is twelve centimeters, giving us a speed of light of
.
The accepted value is
.
So that's pretty good! At the meeting, we got a wavelength of around 20 cm, and I'm afraid I'm not really any closer to knowing why, unless we just didn't properly wet the fax paper.
My second run was even better:
You can actually see that there is a standing wave in both the horizontal and vertical directions (at least, that's what I think this is showing). There are three blobs in the vertical direction spaced about six centimeters from one another, and two in the horizontal.
Very cool.
-Tim
While nothing I did here was exceptionally dangerous, there is still some risk of damaging your microwave or setting fire to the paper if you tried this yourself. Please do not try this at home.
(If the images and movies load too slowly or not at all, try going here.)
We used the fax paper method since it would be the cheapest and make the least mess. (Like we really wanted 600 students handling chocolate bars or eggs in there all week.) Anyway, here's what you need:
- A microwave oven
- Thermal fax paper
- Paper Towel
- Pyrex dish
- Ruler
where c is the speed of light (which we're trying to get), f is the frequency of the microwave and lambda is the wavelength. Remember that microwaves are electromagnetic waves, just like light, and so they always travel at the speed of light.
So how do we measure the wavelength? Well, the way that a microwave cooks food is by setting up a standing wave inside the oven. Basically, microwaves are created by a device called a magnetron and shot into the main chamber. Then the waves reflect off of the metal walls and screen covering the door. This bouncing around sets up a well defined pattern of waves, called a standing wave. In one dimension, a standing wave just looks like a sine function,
In some places, the amplitude of the wave is large, meaning the electric field part of the wave is oscillating up and down at full strength, and in other places the amplitude is zero. The food in the microwave is cooked because the changing electric field forces the water molecules in the food to flip back and forth with the oscillation, heating the food. Conversely, the areas where there is no oscillation don't get heated. This is why your microwave rotates the food as it cooks, so that no part of the food is stuck in a place where it won't be cooked. The movie above shows one wavelength of a wave, the wavelength is the minimum distance it takes for the wave to repeat itself. Notice that the distance between the two peaks is half of a wavelength.
Our method for measuring the wavelength was to take some fax paper, which changes color from white to black when heated, and lay it over a moist paper towel on top of an upside down pyrex dish, like so
The only difference between what we did at the meeting and how I did it at home was that I made sure to press gently on the fax paper so that it was uniformly moist before starting. Then I just ran the microwave for about 15 seconds. The microwave heats the water and causes the fax paper to turn black. The idea is that we should be able to see a pattern of black spots where the microwaves have the highest amplitudes and that the distance between two spots will be half of the wavelength of the microwaves in the oven.My first try produced this:
Two splotches, six centimeters apart. Which means that the wavelegth of the waves in the microwave is twelve centimeters, giving us a speed of light of.The accepted value is
.So that's pretty good! At the meeting, we got a wavelength of around 20 cm, and I'm afraid I'm not really any closer to knowing why, unless we just didn't properly wet the fax paper.
My second run was even better:
You can actually see that there is a standing wave in both the horizontal and vertical directions (at least, that's what I think this is showing). There are three blobs in the vertical direction spaced about six centimeters from one another, and two in the horizontal.Very cool.
-Tim
While nothing I did here was exceptionally dangerous, there is still some risk of damaging your microwave or setting fire to the paper if you tried this yourself. Please do not try this at home.
(If the images and movies load too slowly or not at all, try going here.)
posted by tjmcardl | 9:40 PM
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