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Measuring the speed of light with chocolate and a microwave oven

Written by Jasper on October 5, 2008 · View Comments

Here’s a great excuse to eat a lot of choco­late in the name of science.

Standard electromagnetic (light) wave.

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.

mmm... gooey...

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.

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Categories: DIY Science, Electromagnetism - Tags: , ,

  • 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.

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  • 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

  • http://blarneyfellow.wordpress.com/2010/01/14/links-for-2010-01-13/ links for 2010-01-13 « Blar­ney Fellow

    […] 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:
    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 )

  • 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

    […] Read it. […]

  • 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.

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  • maya

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

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  • Fuck U Bitches

    lol

  • Fubitches

    Hey fuck off tats my name

  • Jon Singer

    How about this glass white­board to add to the mix?

  • 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

  • http://www.facebook.com/profile.php?id=100001021044733 Jesse LaBossiere

    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

    What will be the debate about this experience?

    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?

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