Here’s a great excuse to eat a lot of chocolate in the name of science.
First of all, you need to understand that microwaves are just electromagnetic waves with a certain frequency and wavelength just like visible light. Wavelength is the length between consecutive peaks of the wave. It’s a very intuitive name. You can see it labeled in the picture to the right as the Greek letter “lambda” (λ). Since waves propagate (move), we can also define a quantity called the frequency. Frequency is the number of peaks of a wave that pass a certain fixed point per second. Wavelength is a measure of distance, and frequency is a measure of one divided by time. So to find the speed (“c“) of the wave, you just need to multiply these two quantities together:
c := speed = (distance) x (1/time) = (frequency) x (wavelength)
…but why the chocolate and the microwave, you ask?
What you need to do is use a microwave oven and a piece of chocolate to measure the frequency and wavelength of microwaves. Then you can find the speed of light! Fortunately, microwaves usually have the operating frequency written on the back. Check the back of your microwave. Mine says the frequency is 2450 MHz ( = 2,450,000,000/1 second).
Now that we have the frequency, all we need is the wavelength; this is where the chocolate comes in handy… You might have a microwave with a spinning dish inside. You can probably guess what that’s for. It’s to help heat things up evenly (like stirring a pot of soup on the stove). Whereas on a stove the heat is concentrated on the bottom of a pot, the energy (and thus heat) that microwaves give to food is concentrated at the peaks of the microwaves (which are standing waves in a microwave oven). If we take out the rotating dish then we can find these peaks, measure the distance between them, and find the wavelength. So we just need to heat the chocolate up a bit, find some soft spots (where the peaks of the microwave standing wave are) and measure the distance between them with a ruler.
Here’s what you’ll need:
- Large chocolate bar (bigger than 5 inches)
- Ruler (to measure distances)
- Microwave oven (with rotating dish removed)
- Coffee (optional… it goes well with chocolate)
Place the chocolate bar (unwrapped) in the microwave oven and heat it up (without moving it) until you can see soft spots forming. If I were to hazard a guess for the timing, I’d say heat about thirty seconds… but that’s a guess. It really depends how powerful your microwave oven is.
When you have at least two soft spots forming in the chocolate, take it out and try to measure the distance between them with a ruler. (I had to prod the chocolate lightly with a spoon to find the soft spots). My chocolate didn’t turn out very nicely, but I was able to make a very rough measurement of about 4.5 inches between the centers of the soft spots. 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.
Now we can use the wonders of Google to do the calculations for us. I can just type the following right in Google and it will calculate the speed in the proper units: “2450MHz*4.5inches“.
Google says:
(2450 megahertz) * 4.5 inches = 280 035 000 m / s
…but how close are we to the real answer, you ask?
We can check our answer with Google again. Just type “c” into google and it will give you the speed of light!
Google says:
the speed of light = 299 792 458 m / s
For a measurement made with a ruler and a chocolate bar, it’s not too far off. It works!
But don’t take my word for it, listen to this amateur scientist explain the experiment.
Measuring the speed of light with chocolate and a microwave oven …………. and google….
@pbrain
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You can use a pencil and paper instead if you want to
There is something strange about the interpretation given for this experiment. The distance between anti-nodes in a 1D standing wave should be lambda/2, not lambda. Of course, without knowing the detailed 3D standing wave pattern inside the microwave cavity it’s impossible to derive a quantitatively correct value for c. I think the fact that, in this case, the product of measured distance and frequency is close to c is just fortuitous.
I agree with Lord Axil. For a standing wave, peaks become valleys and valleys become peaks after reflection. There is energy in both spots, so the separation of hot spots should be lambda/2. The 3D pattern will not create anti-nodes (peaks and valleys) which are separated by one wavelength. This is bad physics, which perpetuates misconceptions.
Yes. Thank you both. I’ve made note of that after the fact in bold red.
As interesting as this experiment is, unfortunately it does not prove anything about the speed of light.
That frequency you see printed on the back of a microwave? The manufacturers don’t measure it directly. Instead, they measure the wavelength of the antenna they built inside their microwave, and take the published value of the speed of light and work that equation the other way to derive the frequency.
So when you take the same measurement, and use that printed value that was actually derived from the “unknown” variable, and plug it back into the same equation, of course you wind up with the same “unknown” variable the manufacturer started with. You’ve learned nothing new, sorry.
@Realist
Well… be realistic. What do you expect? This is done with chocolate in a microwave oven! I think you have high expectations of chocomeasurement. The value of this experiment is not measuring the speed of light… it’s learning the steps involved in scientific investigation (while eating chocolate) and hopefully learning something about the nature of light too.
The speed of light is a defined fundamental constant. And the meter (length) is defined from it. So perhaps, if one wanted to be pedantic, it would make more sense to measure the frequency of light used in a microwave oven from the definition of the speed of light and measurement of its wavelength using chocolate.
Great article as well as interesting. Thanks
I’m a little lat3e, but this is very cool
A couple thoughts:
1) The spinning tray isn’t the only thing added to produce even heating. There is sometimes a fan as well. Since it worked, I’d guess yours did have one, but it’s a possible that others might run into.
2) c is the speed of light in a vacuum. It’s usually good enough as an approximation for the speed of visible light in air, but is it good for the speed of microwaves in chocolate? I’m guessing the crudeness of the experiment is the real reason, but this could account for some of the discrepancy.
In reply to @MRW 2), your measurement of the distance between soft spots creates a lot of uncertainty in your result– you just can’t measure that well. As a result, the speed of light in a vacuum is a perfectly reasonable assumption. (I’m talking air, here; the microwaves don’t really travel through the chocolate at all, they just transfer energy to it after traveling through the air to reach it.)
real cool I must say I used for a sciencee project and got a 1 place THANKS!
@ScienceFreak98
Great job!
I hope the prize was as good as the chocolate!
it was if not better Thanks AGAIN!!!!!!!!!!!!!!!!!!!!!
it was if not better
Sounds similar to this high school class:
http://www.physics.umd.edu/icpe/newsletters/n34/marshmal.htm
Finding the Speed of Light with
Marshmallows-A Take-Home Lab
Robert H. Stauffer, Jr., Cimarron-Memorial High School, Las Vegas, Nevada, USA
I have heard that at 16 years old, Albert Einstein constantly wondered what it would be like to ride on a beam of light. Students in physics always seem to be fascinated by the properties of light. However, speed-of-light demonstrations often require extensive preparation or expensive equipment. I have prepared a simple classroom demonstration that the students can also use as a take-home lab.
The activity requires a microwave oven, a microwave-safe casserole dish, a bag of marshmallows, and a ruler. (The oven must be of the type that has no mechanical motion-no turntable or rotating mirror. If there is a turn-table, remove it first.) First, open the marshmallows and place them in the casserole dish, completely covering it with a layer one marshmallow thick. Next, put the dish of marshmallows in the microwave and cook on low heat. Microwaves do not cook evenly and the marshmallows will begin to melt at the hottest spots in the microwave. (I leaned this from our Food Science teacher Anita Cornwall.) Heat the marshmallows until they begin to melt in four or five different spots. Remove the dish from the microwave and observe the melted spots. Take the ruler and measure the distance between the melted spots. You will find that one distance repeats over and over. This distance will correspond to half the wavelength of the microwave, about 6 cm. Now turn the oven around and look for a small sign that gives you the frequency of the microwave. Most commercial microwaves operate at 2450 MHz.
All you do now is multiply the frequency by the wavelength. The product is the speed of light.
Example:
Velocity = Frequency ´ Wavelength
Velocity = 2450 MHz ´ 0.122 m
Velocity = 2.99 ´ 108 m/s
This works in my physics class, often with less than 5% error. Then the students can eat the marshmallows.
(Reprinted with permission from The Physics Teacher, vol. 35, April 1997, p. 231. Copyright 1997 American Association of Physics Teachers )
We used to do a similar demo using a line of chocolate chips set on a wooden (non-heat-conductive) ruler. You can usually get several melted spots, and the measurement is easy. And then you have extra chocolate chips to hand out to the kids. Your version sounds less messy, though.
Another scientific thing to know is that the more times you heat and cool chocolate, the lesser its quality becomes. So, make sure you only do this once with any piece of chocolate, and eat it before it cools to ensure no more quality is lost.
Neet experiment. I might try it. Just a few reflections. There is no right answer, such as what you will find in a book. Your measurement is as valid as any. Any number for a measurement must be accompanied by historical data regarding how the measurements were taken, etc. There is no “correct” number for the speed of light.
Second, you rely on a frequency measurement on the back of the microwave, but that may have been determined assuming a particular speed of light. You don’t know how that number was derived, what experiment or measurement was used. So it may be circular reasoning to use that measurement to determine the speed of light. I recommend skepticism regarding measurements taken from the back of a microwave.
great project. it helped me a lot. did something similar for my science fair project.