How To Measure the Speed of Light... Using Chocolate!

Step 5 Now for the mathy stuff.

Ok, now that we know the distance between hot spots, we'll use some math, and some science, and some more math to figure out the speed of light. First, the distance that we measured represents the half-wavelength of the waves being emitted by the microwave (according to the book). To find the wavelength of the microwaves, we multiply by two. In my example, that gives us a wavelength of

7.628 cm * 2 = 15.256 cm

Now, since the speed of light is equal to the wavelength times the frequency, we can figure out the speed of light. But we don't know the frequency of the microwaves. Apparently, most microwaves operate at 2.45 gigahertz, or 2,450,000,000 Hz. So, we take the the product of the wavelength and the frequency:

15.256 cm * 2,450,000,000 Hz = 37,377,200,000 cm/s which, given that we are doing this in a kitchen (and a small error our measurements are multiplied by 4,900,000,000), is shockingly close to the actual speed of light, which is 29,979,245,800 cm/s, or, as it is typically defined, 299,792,458 meters per second.

Comments

[tpobrienjr]

My son, the PhD Physicist, is doing this experiment with his kids this weekend. If they do it a lot, they can take an average. That's a lot of chocolate.

An alternative: a neatly spaced array of M&Ms would give an indication of the hot spot pattern in the microwave. Science Fair, here we come!

[AL1967]

Hi All I have been buildinng Tesla Coils as a hobby now for about 8 years and i once read that the speed of light is 300,000 KM per second

[knektek]

I read that light beams from the Sun takes 8 seconds to reach the Earth's atmosphere.

[chiron1]

Actually, it takes approximately 8.5 minutes, not seconds.

[Xellers]

Its actually about 300,000 meters per second, not kilometers. You can get a precise answer for this using Maxwell's equations. That is why we know that the speed of light is a universal constant.

[biboNL]

it is not a universal constant, they have been able to slow light down to about 0.1 miles/s, google "bose-einstein condensate" or "BEC".

[awang8]

Actually, it is about 300,000kms per second. That's equal to 3 million metres per second.

[ac7ss]

You are missing a decimal point... 3*10^5 km/sec = 3*10^8 m/sec, or 300 million m/sec. (Close enough for most math, it's what we used for critical point calculations on the reactors.)

[ac7ss]

aarg markup errors. should read.
3*10^5 ^ km/sec = 3*10^8 ^ m/sec

[skizzilini]

300,000 KM/s is an approximation. 300,000Km/s is just an "easy" number for equations, i.e., easy to remember. It's useful when you're taking tests and things. But the actual speed of light in a vacuum is, as of our current technology, a bit slower.

[biofueljunke]

be a great bet at a party you could win some cash

[kd1s]

Oh yeah, almost completely forgot to mention the little thing about a transmission medium. There' s a thing called the velocity factor that is in play. Ie, how close to the speed of light does it get. In the real world a waveguide has a decent velocity factor.

[bradpowers]

Well, I was 25% off. I have no notion of what effect the transmission medium had. Nor do I care, because I got to eat warm gooey chocolate, and was on the right order of magnitude.

[kd1s]

I suppose that's true. It's just the transmission medium in this case would be air, which is comprised of many different things. If I recall correctly the vf of air is 1. But gooey chocolate does sound good.

[haoran]

The assumption in this experiment (or at least, in measuring the results of this experiment) is that the microwaves travel along the length of the bar of chocolate. When, in fact, it could be at an angle. If you were to take a larger wide block of chocolate, then you could measure hotspot as a point, rather than as a line perpendicular to the bar of chocolate, no?

[bradpowers]

True, but I'm at Instructables HQ, and the chocolate bar that I used for this experiment was chowed down on until that was all that was left. :)

[jaem]

All the microwaves I have seen have their frequency listed on the label on the back. You might want to add that as a suggestion to try before guessing it. But yes, I believe they tend to be around 2.4-ish GHz.

[Unkat]

After seeing the episode of MythBusters where one of the titular protagonists tries to assemble a super-microwave machine, I get the impression that the actual waves are often generated in one place (located behind the control panel) and shot into the chamber to bounce around as they will. Which means that if you knew exactly where and in which direction these waves were generated, you could line the chocolate up parellel with and directly in the path of the waves, thus achieving quite an accurate measurement (leaving out various other human errors, like getting chocolate in your calipers). Cheers man, funny instructable. ~U

[srilyk]

That's exactly why you have the turntable in your microwave oven, because basically the radiation bounces to particular spots, creating "hot spots" in your food.

Which is also why you take it out for this experiment!

Yay science!

---

This was a great instructable!

[kd1s]

And getting the wavelength one only has to use this formula:

Wavelength = 300 / f where f is frequency in MHz and the wavelength is in meters.

[hyraspray]

Obviously you can work out the wavelength if you already know the speed of light! You've put it in your formula: 300. The whole point of this instructable is to measure the speed of light.

[powerfool]

Wait! I don't get it! Why is the distance between the hot spots half the wavelength emitted by the microwave oven?

[shovemedia]

Ever swing a rope with partner? Then try it double-time? If you do, you'll get a (relatively stationary) node in the middle of the rope (and at each end where the rope's being held). You also get wildly gyrating sections in between with one maximum 1/4 of the way from you, and the other 1/4 of the way from your friend. When the max at your end is high, the max at the other end is low (and viceversa). and it looks like a tilde: ~ That's one wavelength. The microwaves are doing the same thing. The chocolate at the microwave's nodes form hot-spots because the energy passes through those points most of the time compared to the other areas where it's more spread out in 3d space. If you follow the ~ shape of the jumprope and the location of it's nodes -- you should be able to see how the distance between two nodes is only half the wavelength.

[kgtateddy]

maybe because it affects boths sides of the chocolate and not just the left or the right one. So that makes *2

[powerfool]

But still I don't understand how the hot spots are related to the wavelenght of the microwaves! One thought would be that the microwaves are reaching their maximum amplitude at the hotspots however the microwaves are not emmitted parallel to the chocolate so that we could say that (the axis of motion is not parallel to the chocolate) and also there are many reflections inside the oven and I guess the microwaves are reaching the chocolate (and the hot spots) at many different phases. Right? But I want to eat chocolate now and it's too late at night here... :((

[shovemedia]

hadn't thought of that -- but i think most microwaves actually do a terrible job spreading (bouncing) the energy around; there's almost always hotspots which is why even the cheapest little microwaves have rotating plates.

I think this article assumes that you'll probably get "lucky" and have a stream of energy that *is* more or less parallel to the chocolate.

Hmm...so maybe you could "map" the intensity of the oven across 3d space
if you had enough chocolate and an adjustable platform? No good will come of this... what's that smell?

[fentanyl3]

they actually do an extremely good job of reflecting the waves around, the problem is not reflection, or lack of it, the problem is standing waves. as the magnetron is running, the mean frequency emitted creates standing waves inside the box which is what creates the hot spots, this experiment is highly unrepeatable due to the fact that you might actually be measuring two separate standing waves. Take a small glass of water and place a vibrating object into it, it will create waves that interfere with one another, and others that add to each other which will give you an overall increase in the area that are additive. this is what happens inside the box

[pachequin]

HI! I have a question: Why do you have to multiply by 4,900,000,000? I do not get where that number came. Thanks.

[saintneko]

You don't - he said *errors* are multiplied by 4.9 billion times. (because light is so fast and our measurements are so small)

[JeeCee]

2 times 2,450,000,000

[blue66]

LOOOOOL

[PyroManiac96]

...well its better than just guessing the speed of light (i was off by like a billion when i guessed)

[bradpowers]

Hey, being off by 7 million m/s isn't so bad. Right?