Measuring the speed of light with Chocolate Chips

Posted by Matthew Fri, 10 Mar 2006 07:41:00 GMT

Over the past week, I’ve been really busy with exams and projects. Trying to save time by finding the speed of light on Google, I stumbled upon an extremely interesting article on measuring the speed of light with a microwave. As any decent cook knows, microwaves do not heat evenly. In fact, this article explains their heating patterns are relative to the speed of light!

Understanding how a microwave heats

As we all know, microwaves heat using electromagnetic waves. These waves are at a frequency perfect for rotating water molecules (f = 2.5 GHz). The rotating water molecules create friction and thereby heat.

Two types of electromagnetic waves

Although there are two types of electromagnetic waves, we typically only consider traveling waves. The amplitude of the wave travels forward in position over times. The following animation demonstrates the amplitude of a wave over space and time.

A traveling wave
Chocolate chips

The waves in a microwave are not traveling. If they were, it would be nearly impossible to distinguish any uneven heating patterns!

Standing waves in a microwave

The waves in a microwave oven are standing waves. These waves are stationary in space with an amplitude changing over time.

A standing wave
Chocolate chips

With this demonstration, it is obvious that particular sections of the chips are heated more than others. In fact, these locations are located half of the wave’s length apart.

The physics of waves

We now know the frequency of the microwave and can presumably measure the length of the wave, but how are they related to the speed of light? Simple. Electromagnetic waves propagate through free space (like that in a microwave) at the speed of light. Therefore, their length is related directly to the speed of light by λ = c / f where λ is the wavelength, c is the speed of light, and f is the frequency of the microwave. Solving for the speed of light, c = λ * f.

Where do the chocolate chips come in?

Chocolate chips are perfect for measuring the distance between melted spots. The heat does not spread as quickly through them because they are not uniform. This means the melted spots will be smaller and you will have more time to measure before they all start to melt.

Melted chocolate chips

It is hard to tell from the photos, but there were distinct melting spots almost exactly 6cm apart. Remember, this is only half of the wavelength, so λ = 12cm. Plugging all the known variables into our equation, we get c = 12x10^-2 * 2.5x10⁹ = 3x10⁸. Not bad! The true speed of light is 2.9987x10⁸.

Notes if you replicate this experiment

The chocolate chips only take 20-30 seconds to melt. The longer you have them in, the bigger the melted spots will be and the less time you will have to measure.
This will not work in a microwave with a spinning carousel. In fact, the microwave spins to counteract these effects. Usually, you can just flip the carousel upside down to stop it from spinning. (Thanks Ryan)
If you plan on putting the chips back in the bag, simply refrigerate them. Freezing causes them to stick to the plate.
You can microwave anything that melts. (Cheese or a chocolate bar) However, chips work particularly well.

Photo gallery

Comments

Leave a response

errwa said 1 day later:

Wow This is some real geekness! Thanks for posting.
Dave said 1 day later:

Nice demonstration!

I’d correct the math, though: 12 cm is NOT 12x10^-3 The result, 3x10^8, is right, but you can’t get there from 12x10-3

Dave
Ryan Gardner said 1 day later:

Yeah, I agree with Dave… I smell some fudge in this chocolate calculation.

I had a professor do this with marshmallows once… he let it go for a while so that you could clearly see where the nodes were when he showed it to us as a class. It was harder to get a precise reading on where it was…

I also hope your microwave plate isn’t of the spinning variety…
Matthew said 3 days later:

Thanks. I actually had to stop my microwave from spinning, but I forgot to leave a note about it.

Also thanks for the mathematical correction. I must have been concentrating more on the HTML superscripts than the actual numbers I was typing!
Doubter said 4 days later:

Don’t most microwaves also have a spinning platter that could throw this off?
nate said 4 days later:

Be careful, carmalized sugar sticks and is very hot. Don’t burn your fingers.
s said 4 days later:

Very cool. Only minor point: speed of light is 2.9979x10^8, not 2.9987x10^8.
Saltation said 5 days later:

My Trackback ping keeps bouncing so here it is in Comment form. This post referred to your site:

Speed of Delight
Hello, everybody! Professor Sal “Astro” Gation here!, bringing science into YOUR home. Everyone needs science, especially busy househusbands and lazy businesswomen, who can easily run out of science halfway through the afternoon with no chance to nip down to the labs.
…
codelieb said 5 days later:

This is a fun experiment, but to call it “measuring the speed of light” seems to me somewhat circular reasoning. The experiment is predicated on knowledge of the frequency of radiation in a microwave oven. How do we know that? Suppose we are given a detailed design of a microwave oven. Is it possible to figure out the frequency of the radiation without using the speed of light in your calculation? (Not if you use Maxwell’s equations or anything that follows from them.) On the other hand, suppose you just had some kind of a meter to measure the frequency of the radiation in the oven, so that you don’t have to make a calculation of the frequency to know what it is. Okay, then… how was that meter designed? Did it involve, per chance, use of the speed of light in some calculation? Very probably. So it seems to me that knowledge of the speed of light is, in practice, prerequisite to the knowledge of the frequency of the radiation in the oven.
Fred said 5 days later:

This isn’t a speed of light measurement as claimed. It is a wavelength measurement (measurement of the wavelength in air) from which the speed of light can be calculated using the wavelength-frequency relationship. Light wavelength can also be obtained from a coherent laser and measuring the distance between interference fringes.
Kay M Purcell said 6 days later:

Modern electronics allows frequency counters to be made by sampling the voltage and counting the zero crossings. Of course the sampling rate would have to be 5 GHz or greater. No calculations involving the speed of light required. Although it is difficult to see how this sort of device could be used in a region of standing waves.
Margarita said 6 days later:

Man you guys are major nerds but like loving the hole chocolate chip thing it totally made me hungry!
Mordecai said 2 months later:

you should be more careful with your links…. you forgot an “_p” right before the “.htm” –made your source a real pain to get to. Also, you say that the microwaves are standing waves… so why are you talking about them having a speed?
Mordecai said 2 months later:

*ok, maybe your link wasn’t the problem… I found the _p on google… but it didn’t work either.
Matthew said 2 months later:

The internet can be a real pain sometime! The About.com link is dead now. I am proud to be keeping this experiment alive, though.

Speed defines the time it takes for the standing waves to rise and fall. It may not be very technical terminology, but it suffices. I don’t think it is misleading.
sonumol said 2 months later:

i think this is a great experiment. i actuallly used this experiment for my year long physics project. this article was very helpful.
mehreen said 6 months later:

Hello I am a student at the University of Mauritius. I am doing my final year project on chip present in microwave oven. If ever you have some information on the chipset and the name and properties of different microwave chips sent it to us on mehreenjoom@hotmail.com. Thank in advance
Sidra Iqbal said 8 months later:

i thinkk this is a good information about how can we measure the speed
nancy at lc said 9 months later:

I tried this with the chips at home and it worked great. I used it in my class with a large chocolate bar, and it didn’t work as well (we were off by over 2x the speed of light). So stick with the chips!
YO YO in the fridge said about 1 year later:

Too COOL! I hadthe most fantastic time with the studying of the speed of light. This experiment was exciting and more than ever interesting!
Jack Mullet said about 1 year later:

Wow unbelievable, although there was one problem with one of the measurements. It should be 12*16 dimensional to the protractor and the plate must be standardised steel with the high heat of the microwave which causes the chocolates to melt quicker than anyone could anticipate. But for the most part, i really enjoyed this project.
Lanny Barbie said over 2 years later:

that’s a great article!
Matthew S said over 2 years later:

We could take the microwave apart (or a similar one we don’t need anymore) and reverse the electronics to learn what the frequency is from whatever timing source your microwave uses (or reading the label on the transmitter)

Cool experiment, I’ve got a 10 year old who will find this exciting and tasty.

Thanks
MikeHersee said over 2 years later:

My mate and I tried it with a big bar of Cadbury’s chocolate. To our disappointment our first noticeable gap between melting points came in at about 11 cm, thus his microwave was allegedly producing microwaves at nearly twice the conventional speed of light. We tried it for longer but it ended up making the whole bar liquid without giving us any more measureable points. So we decided next time we’d used chocolate chips, and spread our melted chocolate bar all over some cherry ice cream instead.
Beefyboy said over 3 years later:

my experience with this test is that all of the modern microwaves randomize where the radio waves are. Are you aware of any microwaves with standing waves that remain in the same place?- other than that- great experiment!
rapidshare said over 3 years later:

wow, that’s awesome! have no words to express my feelings:) it’s an unbelievable site. so many outstanding pieces of information. thanks for posting this!

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Forwarder said over 3 years later:

I tried this with a bar of cooking chocolate,which is plain rather than milk. As it melted quite fast, I had an idea and got a bag of marshmallows. I then dipped a marshmallow into the molten chocolate and was forced to eat it as I couldn’t help myself. So much for scientific experiments involving chocolate!

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Katy said over 3 years later:

Hi I did this as well and found that the hotspot was in only one area. What is the explanation for that
For Your PC said over 3 years later:

I always wanted to understand how it works! Thanks!
Greg said over 3 years later:

Modern microwaves randomize where the radio waves are.great experiment though! http://filepasswords.com
Orkut Scraps said over 3 years later:

As interesting as this experiment is, unfortunately, proves nothing about the speed of light.

This frequency is printed on the back of a microwave oven? The manufacturers do not directly measure. Instead, measure the wavelength of the antenna is built into your microwave, and take the published value of the speed of light and the work the other way to obtain the frequency equation.

So when you take the same measure, and use the printed value is actually derived from the variable “unknown”, and reconnect in the same equation, of course ending with the same “unknown” variable began with the manufacturer. Have you learned anything new, sorry.

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digital camera brisbane said over 3 years later:

Interesting read, thanks for helping keep me busy at work ;)
Road Trip said over 3 years later:

I tried this with a bar of chocolate for cooking, which is simple instead of milk. As it melted very fast, I had an idea and has a bag of marshmallows. Then came a marshmallow in melted chocolate and was forced to eat, since I could not help it. Both for scientific experiments on the chocolate!

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Hollywood Wallpapers said over 3 years later:

Place a plate with a single layer of marshmallows in a microwave dish-free, and ZAP to some of them are just beginning to melt. Measure the distance in centimeters between the melting points, but should be about 6 cm. Below is a signal with the frequency of microwaves, typically 2450 MHz With these two data, the speed of light can be calculated through Speed = Frequency x wavelength. Chocolate shavings or other substance that melts very well be replaced.
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So friggin cool, now I can apply all this great strategy and become a winner :)

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The thought of melting chocolate makes one feel rather peckish!
Utah heating contractor said over 3 years later:

generated by counting the number of C subα/sub atoms in the two predictions within 3.5 Å of each other after being superpositioned

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