Measuring the speed of light with chocolate and a microwave oven

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”.

(2450 mega­hertz) * 4.5 inches = 280 035 000 m / s

We can check our answer with Google again. Just type “c” into google and it will give you the speed of light!

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!

Post Revi­sions:

There are no revi­sions for this post.

• http://morningcoffeephysics.wordpress.com/2009/01/22/adventures-of-the-learning-assistant-part-1/ Adven­tures of the Learn­ing Assis­tant (Part 1) « Morn­ing Cof­fee Physics

[…] tube. The physics and process behind that exper­i­ment is com­pletely anal­o­gous to my post about mea­sur­ing the speed of light with choco­late and a microwave. They will use a micro­phone to find the pres­sure nodes (quiet bits: reverse ana­log of the soft bits […]

• pbrain

Mea­sur­ing the speed of light with choco­late and a microwave oven .….….…. and google.…

• http://morningcoffeephysics.wordpress.com Jasper

@pbrain
You can use a pen­cil and paper instead if you want to .

• Lord Axil

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.

• http://universio.wordpress.com/2009/02/27/mustien-aukkojen-olemisen-sietamaton-keveys/ Mustien aukko­jen olemisen sietämätön keveys « uniVersI/O

[…] että val­olla on jokin äärelli­nen nopeus, ja nykyään sen voi itse hel­posti todis­taa vaikka suk­laalla ja mikroaal­tou­u­nilla. Kokon­aan toinen asia oli kuitenkin se, tun­teeko valo pain­ovoiman vaiku­tuk­sen, eli onko se jonkin […]

• Physics Teacher

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.

• http://morningcoffeephysics.wordpress.com Jasper

Yes. Thank you both. I’ve made note of that after the fact in bold red.

• Real­ist

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.

• http://morningcoffeephysics.wordpress.com Jasper

@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.

• http://www.cheapmicrowave.org/ Robert Rod­er­ick

Great arti­cle as well as inter­est­ing. Thanks

• MRW

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.

• ScienceFreak98

real cool I must say I used for a sci­encee project and got a 1 place THANKS!

• http://morningcoffeephysics.wordpress.com Jasper

@ScienceFreak98
Great job!
I hope the prize was as good as the choco­late!

• ScienceFreak98

it was if not bet­ter Thanks AGAIN!!!!!!!!!!!!!!!!!!!!!

• ScienceFreak98

it was if not better

[…] Mea­sur­ing the speed of light with choco­late and a microwave oven « Morn­ing Cof­fee Physics ~1min (tags: physics cool) […]

• http://reddit.com schro­ding­ers­bohr

Sounds sim­i­lar to this high school class:

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 )

• speek

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.

• speek

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.)

• http://www.lefrancophoney.com lefran­coph­o­ney

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.

• http://dyspepsiageneration.com/?p=33949 DYSPEPSIA GENERATION » Blog Archive » Mea­sur­ing the speed of light with choco­late and a microwave oven

• http://www.petersnewyork.com Peter

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.

• http://thegreatgeekmanual.com/blog/geek-media-round-up-january-14-2010 The Great Geek Man­ual » Geek Media Round-Up: Jan­u­ary 14, 2010

[…] Morn­ing Cof­fee Physics explains how to Mea­sure the Speed of Light with Choco­late and a Microwave oven. […]

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[…] Morn­ing Cof­fee Physics explains how to Mea­sure the Speed of Light with Choco­late and a Microwave oven. […]

• maya

great project. it helped me a lot. did some­thing sim­i­lar for my sci­ence fair project.

• http://kulmedfysik.wordpress.com/2010/03/05/lite-om-naturkunskap-vid-diskhon/ Lite om naturkun­skap vid diskhon « Stjärn­stoft och kugghjul

[…] Det finns väldigt mycket fysik, kemi och biologi i köket, som bekant. Den här gre­jen om att mäta ljusets hastighet med chok­lad i mikron är ett exem­pel som jag nyli­gen återi­gen sett länkar till (odödligt inlägg, och bloggen Morning […]

[…] exper­i­ment, jag vet att som­liga får göra det i gym­nasiefysiken. Själv tror jag att det var på Morn­ing Cof­fee Physics jag först läste om det (där finns lite diskus­sion i kommentarerna […]

• Fuck U Bitches

lol

• Fubitches

Hey fuck off tats my name

• Jon Singer

• Chrlzem

Chuck’s blog on choco­late light Using dis­cern­ment some of the com­men­ta­tors could use some prac­tice in mm„cm and m. Them in mea­sur­ing time in mil­lisec­onds. Then comes in the expres­sions like X mul­ti­plied by 10 to the 8th. Soon liters and Grams. Wahl your out of the bushes and com­mu­ni­cat­ing like an adult. You choco­late lov­ing dudes need to look on the both sides of you test sam­ple and see on your sam­ple 4 –13/16 inches is on one side and 2– 7/16 is a warm spot on the other side of your sam­ple. Hop­ing most of you will develop thin­ner sam­ples of other medi­ums and bet­ter mea­sur­ing skills.. Please try a Sty­ro­foam food plate with 5 to 6 mm of frozen clean water with a very thin coat­ing of var­i­ous kinds of choco­late. Hint heat water very hot to melt choco­late then freeze . Sci­ence is a huge invest­ment in time . John Wayne said life is tough and a lot tougher if you are stu­pid. I wish he would have used if you use a untrained mind instead of stu­pid. After all it is your mind and only you can train it Think about that for a long time . You only get A’s or less by your lim­its. An A grade is a limit that you learn as slow as the teacher teaches .

• Maya

I am doing this for the Sci­ence Con­fer­ence at my school!

• Peter

The refrac­tive index of the choco­late should also be  taken into account.…

• georgie

What would be the dis­cus­sion for this experiment?

• Anushrut

how can you tell that this is the speed of light in air rather than in chocolate

so mHz x inches = metres?

• Jasper Pal­free

If you mul­ti­ply by a unit con­ver­sion fac­tor it does…

• Julian Ewers-Peters

There is one prob­lem with that exper­i­ment: it does not state the actual fre­quency of vis­i­ble light any­where and the wave­length of vis­i­ble light may be dif­fer­ent from the microwaves in your microwave oven. The results may as well just be a happy coincidence.

• http://wellcaffeinated.net/ Jasper Pal­free

Please see the sec­ond para­graph where I men­tion microwave oper­at­ing frequency

• Glo­ria

I know another sim­i­lar exper­i­ment but you use eggs instead

• Bre­ville

Bre­ville Smart Oven

• smar­toven

I know the expe­ri­ence of other sim­i­lar but instead to use eggs.

Bre­ville Smart Oven

• reyes­david

Great con­cept about work­ing of microwave.

oven spare parts Sydney

• Rose

If you are writ­ing “Mea­sur­ing the speed of light using choco­late” up as an exper­i­ment. What could you say in the conclusion?