## Measuring the speed of light with Chocolate Chips

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.

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.

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.

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 = 12×10-2 * 2.5×109 = 3×108. Not bad! The true speed of light is 2.9987×108.

### 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.

### 32 Responses to Measuring the speed of light with Chocolate Chips

1. nancy at lc says:

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!

2. Dave says:

Nice demonstration!

I’d correct the math, though:
12 cm is NOT 12×10^-3
The result, 3×10^8, is right, but you can’t get there from 12×10-3

Dave

3. Ryan Gardner says:

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…

4. Matthew says:

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!

5. Saltation says:

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.

6. codelieb says:

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.

7. Fred says:

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.

8. Kay M Purcell says:

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.

9. Margarita says:

Man you guys are major nerds but like loving the hole chocolate chip thing it totally made me hungry!

10. Mordecai says:

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?

11. Mordecai says:

*ok, maybe your link wasn’t the problem… I found the _p on google… but it didn’t work either.

12. Matthew says:

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.

13. sonumol says:

i think this is a great experiment.

14. mehreen says:

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.

15. YO YO in the fridge says:

Too COOL! I hadthe most fantastic time with the studying of the speed of light. This experiment was exciting and more than ever interesting!

16. Jack Mullet says:

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.

17. Matthew S says:

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

18. MikeHersee says:

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.

19. Beefyboy says:

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!

20. Katy says:

Hi I did this as well and found that the hotspot was in only one area. What is the explanation for that

21. Rapidshare says:

I have replicated the experiment recently! Yeahh… the chocolate chips only took 25 seconds to melt. You were absolutely right. A very interesting article.

22. freshlook contact lenses says:

Do not touch that dial! And I do not mean the TV line, but the dial on the microwave. I have not used a microwave oven in a while. When I used one I’d always had this gut feeling like something was strange in a strange bright light and wind as the sound strange to heat the food placed in the microwave. I never liked what I did not understand. We do not know the technical details behind how microwave works or how the food is heated, but I do know is for me is natural.

23. Ronaldo says:

Wow This is looking like real geekness.
I guess It is a wavelength measurement (measurement of the wavelength in air), calculated through wavelength = Speed / Frequency. Its really a great experiment though.