Built on Facts

Earlier this week I wrote up a brief outline of an experiment to measure the speed of sound using only your singing talent. I’d like to be able to do the same thing with the speed of light. But it’s a lot harder because light is so friggin fast. As with sound, the speed of a traveling wave c is equal to the product of the wavelength and frequency. If you can find both of those you can find c. Or you could do something like directly measure the time it takes light to travel a specific distance. This is what the early experiments done by Galileo and others attempted without success.

Today it’s doable with pulsed lasers and a decent oscilloscope. I’ve done it myself as an undergrad – bounce a beam of light down the hall and back and divide the distance by the time required to make the trip – a few dozen nanoseconds, generally. But while this is “easy”, it’s not cheap.

But earlier scientists managed it without that technology by carefully measuring the timing of the orbits of Jupiter’s moons. They also pulled it off by doing something similar to the laser pulse measurement where the pulses were both generated and measured with rapidly rotating gear teeth. But that’s neither easy nor cheap, not least of which is because the path required is still kilometers long under the best of circumstances.

So I have no good ideas that don’t involve cheating by assuming prior knowledge of physical information that we can’t measure ourselves. There’s a number of possibilities involving the microwave radiation put out by a microwave oven, but there I’m afraid I think it’s cheating to accept the 2.4 GHz frequency without being able to measure it.

But if you do, you can set rough limits on the speed of light by measuring the size of the microwave oven. The wavelength has to be smaller than the oven itself (maybe 40 cm?) and larger than the holes on the protection screen in the door (maybe 2mm or so). Multiplying those by 2.4 GHz gives an upper limit on c of 960,000,000 m/s and a lower limit of 4,800,000 m/s. Not great, but it’s a start. You could be more precise by measuring the wavelength directly by measuring the distances between hot and cold nodes on microwaved objects.

Comments

#1 Donalbain
April 10, 2009

1) Remove the rotating plate
2) Place a tray in the microwave
3) Place marshmallow bar on the tray:
4) Turn on microwave
5) Wait for ping
6) Measure waves that will be present on marshmallow bar
7) Calculate speed of light
8) ?????
9) ?????
10) Profit!
#2 John H. McDonald
April 10, 2009

If there’s still an analog TV station in your area, you can measure the speed of light.
1) Figure out which building is causing “ghosts” in the image (a rotating antenna will help)
2) Measure the difference between the direct path and the reflected path of the signal going from the TV transmitter to your TV
3) Measure the distance on the TV screen between the main image and the ghost image
4) Look up the scan rate of your TV; or it should be relatively easy to come up with a clever mechanical way to measure this, if you want to stretch the exercise out
5) math
6) c!

See http://astro.uchicago.edu/cara/outreach/resources/ysi94/light.html
and
http://en.wikipedia.org/wiki/Ghosting_(television)
#3 Odysseus
April 10, 2009

Funnily enough, this method was discussed only recently on Scienceblogs.de. Similar to Donalbain proposal, they used a bar of chocolate and found a wavelength of approx. 12cm, which gives quite a good result for c. Still, I agree with you that reading the frequency from the back of the oven is kinda cheating.
#4 rob
April 10, 2009

Donalbain: so that’s where all my marshmallow bars and underwear have gone.
#5 Uncle Al
April 10, 2009

As long as we don’t have to do it ourselves… Laser pointer for light source. A common CPU clock crystal is 40 MHz. SWAG that lightspeed is a foot/nsec. No knowledge of frequency or wavelength is needed.

Run 40 MHz square waves from the first CPU clock to fire the diode laser every other half-cycle (i.e., 12 foot light slug). Laser is focused onto a second, naked running crystal at a shallow angle to reflect onto a distant screen (crystal acting as a vibrating mirror scanner). Pots to diddle phase angle and freq gap between oscillators. What is the sum of the spaced stripes vs. reflection angle and distance?
#6 Nathan
April 10, 2009

This experiment is eminently doable. A couple of my friends in the CU physics department did it a few years ago: http://www.fightingfeynmans.com/vault/sciday/1/microwave1.html
#7 meichenl
April 11, 2009

If you believe light is an electromagnetic wave, you can calculate c from any number of simple experiments using just some wire and a current source, maybe a capacitor, etc.
#8 arkadaslik sitesi
April 11, 2009

thankss.
#9 Geoff
April 15, 2009

I think this could work, although it may be too error sensitive:

1) Set up a lightning rod somewhere with good visibility.
2) Go someplace far enough away (3 km or so?) that there will be a measurable delay for the thunder. Measure the exact distance (d) to the lightning rod.
3) Wait for a thunder storm.
4) When a bolt of lightning hits the rod, record the time delay (t) .
5) Use some other method to determine the speed of sound(v).

The speed of light should then be:

c = 1/(1/v-t/d) = v/(1-vt/d)

Of course, here vt/d ~ 1, so it will be very sensitive to error. d can be measured fairly accurately, so clearly the time delay will be the source of error, and it will probably run into the reaction-time problem. Anyone care to do the error analysis to see if human reaction time is small enough to get a good value out of this?