MEASURE THE SPEED OF LIGHT AT HOME

MEASURE THE SPEED OF LIGHT AT HOME

By Ernest Ventura 18 August 06

Equipments

• microwave oven [with the manufacturer label visible]
• Preferred: 3-4 pieces of sliced cheese [e.g. Kraft Singles]

Alternative: flat chocolate, marshmallows

• microwavable plate
• ruler [preferably metric]

Time Requirements

>1 minute to set up equipments

>1 minute to perform the experiment

Description

This experiment demonstrates how to verify the speed of light using a microwave oven and sliced cheese.

Procedure

1. Remove the turntable from the microwave oven so we can measure the distance between the hotspots accurately. Just go ahead, this initial step will make sense as you go.

2. “Microwave” about 3 or 4 sliced cheese [placed evenly on the plate of course] for about 20 seconds. Just enough time to see 2 or more spots where it begins to melt. If you use marshmallow or chocolate, time may vary but as long as you get at least 2 melted spots, you’re fine.

3. Measure the distance between the hotspots, preferably in centimeters. This is half the wavelength of the microwaves generated inside the oven while operating. You’ll get an explanation why later.

4. With this information, “c” is just a few algebra away using the following relationship:

Speed of light = wavelength * frequency [c = λ * f]

That’s it! You’re done with the experiment. Now what? So where’s the speed of light? Now you do the Math. Depending on your scientific & mathematical “geekness”, you may or may not need to refer to the calculations I provided at the end, based on my own experiment. It turned out virtually ideal so it will serve a good guide when you do this on your own. Be warned that if my measurement of the “distance between the hotspots” [from step 3] don’t match your’s, it doesn’t necessarily mean there’s something wrong. You might be using a microwave oven with a different operating frequency than mine. So just go plug & chug your numbers & check your final value for “c”. It’s not that bad to multiply. Is it?

Aren’t you proud you’ve measured the speed limit of the universe? How happy will you be if you actually know what’s behind-the-scene!

How it works?

When operating, your microwave oven generates electromagnetic waves with frequencies around 2450 megahertz. These waves follow Simple Harmonic Motion [SHM].

If you pluck a guitar string, it will vibrate. Usually, you will excite the “first harmonic”. With effort, you might be able to excite the second harmonic.

Sine wave

A full wave is shaped like a “sine function” going from zero to a positive maximum back through zero to a negative maximum and back to zero again [like the 2nd harmonic]. So you can see that the distance between the maximum displacements of the wave is one half one wavelength. [See the similar diagram below where the hotspots are indicated.]

Simple Harmonic Motion

The electromagnetic field inside the microwave behaves in roughly the same way [as plucking the guitar string causing it to vibrate] – except the vibrations are in “the electromagnetic field”. Where the vibrations are greatest (at the antinodes [a]), you will see the greatest heating, but at the nodes [n], the cheese will only melt slowly as heat diffuses into those areas.

Thus, the distance between the melted regions is equal to the distance between the antinodes [a] or equal to half the wavelength.

Caution

Results are consistent when using the same microwave oven and melting the same food. Instances that gives a different measure for the quantity “half-wavelength”:

A) when using the same microwave but melting different food.

B) When melting the same food but using different microwave oven. This is probably due to the different specifications by different manufacturers.

Evaluation

Complexity: the speed of light is very complex. What’s going on inside the oven while operating is also very complicated because we really don’t see microwaves. How the melted spots in the marshmallows and the distance between them represents half the wavelength of the microwave is also not so easy to understand. This demonstration is very easy given that things work well. This is undoubtedly one if not the easiest way to approximate the value c (speed of light).

Repeatability: This experiment should be consistent because the only possible human error that can alter the results is measuring the distance between the melted spots. The microwave oven usually works the same every time so the approximated value of c given by this experiment is either consistently inaccurate or consistently close.

Efficiency: Microwave oven can be found in almost every household. Marshmallows, chocolates, or even cheese can even be eaten after the experiment is done. There is no other way that I can think of to approximate the vale of c any easier, faster, and less expensive than this.

Safety Factor: there is a probably unnecessary but recommended precaution of placing a half glass of water in the microwave – if there is insufficient material in a microwave, you can blow the internal fuses, rendering the microwave inoperable. However, as the microwave then had to heat the water as well, the melting process took longer.

Interestingness: First I was so amazed of “pi”, then there was Euler’s number. Now I have c. These three constants of the universe are amazing. Not only c is a finite value, it is a universal constant and a speed limit.

Physics-related: Light, optics and modern (contemporary) physics

Formulas Involved: speed of light = wavelength * frequency [c = λ * f]

Calculations

I measured λ/2 to be = 6cm = 0.06m

[I converted centimeters to meters since meters is the metric system unit for length]

This is the distance between the hotspots which is equal to the distance between the antinodes [a]

It follows that one wavelength, λ = 0.12 m.

The oven I used operates at frequency, f = 2450*10^6 Hertz [typical]

Using the relationship c = λ * f,

I found c = 0.12 m * 2450 * 10^6 Hertz

Therefore, c = 2.94 * 10^8 m/s

Percent Error

The accepted value for c = 2.99792458 * 10^8 m/s

% error = (c accepted – c calculated) * 100 / (c accepted)

% error = 1.93% [Less than 5% error is close enough]

Acknowledgment

1. Finding the Speed of Light with Marshmallows by Robert H. Stauffer

http://www.physics.umd.edu/ripe/icpe/newsletters/n34/marshmal.htm