How to measure the speed of light with a microwave oven?

[flora88]

I was wondering if it is possible to convert megahertz per centimeter to meters per second so I can compare my data with the speed of light. I want to put my data as the same units as the speed of light. I was wondering what upper and lower boundary measurments to put error limits on your measurment were and what type of calculations are involved.

[deleted-71709]

Hello flora88,

The short answer to your question is no it is not possible to convert megahertz per centimeter to meters per second. Actually, I am curious what you are measuring using the units megahertz per centimeter.

Megahertz is a measure of frequency, that is, how many times something happens per unit of time. 1 megaHertz is the measure for something that changes 1 million times per second. Centimeter is a unit of linear measure. So you are measuring something that changes 1 millions times for second every centimeter. I can't think of any physical system that can be measured that way, unless you have something like a radio frequency generator that is moving and changing frequency as it moves.

Perhaps if you described your experiment, I would have a better understanding of what you are trying to do and I could be of more help.

Ed Neu
Buffalo, MN

[rmarz]

I'm confused by the mixed units as well. Perhaps you are trying to understand the relationship between wavelength and frequency. That is straight-forward, and uses the speed of light in the calculation. it is:

Equation: f * λ = c

where:
f = frequency in Hertz
λ = wavelength in meters (m)
c = the speed of light and is approximately equal to 300,000,000 m/s

In a typical microwave oven, the frequency of the magnetron is usually 2.45 GHz, and the wavelength of that frequency is about 12.25 cm. I still am not sure how one uses a microwave oven to establish the speed of light in air.

Rick Marz

[deleted-71712]

Hi flora88,

For everyone's reference, it looks like you're doing this project:

https://www.sciencebuddies.org/science- ... p056.shtml

and there's a little more background info here:

http://www.physics.umd.edu/icpe/newslet ... rshmal.htm

So, the quantity you measured in cm should be the distance between "hot spots" in the microwave. For many measurements, error is related to the spacing of markings on the measuring device (e.g. mm or half-mm on a ruler), but in this case I bet the size of the hot spots is larger than that and that most of the error comes from identifying the hot area and estimating the location of the center. In that case, you could use the size of the hot spot, or maybe half of that, as an estimate of the error in this distance.

It's unlikely that an error is reported for the microwave frequency. You could either choose to assume zero error, or estimate it based on the rounding in the reported number. For example, "2450 MHz" implies that the frequency is definitely closer to 2450 than to 2460 MHz, but it doesn't necessarily guarantee that it's 2450 rather than 2451 MHz -- so +/- 10 MHz would be a conservative estimate of the error. Then you can look up how to propagate the error when multiplying two numbers to get the error in the speed of light that you calculate:

http://en.wikipedia.org/wiki/Error_propagation

Here's where I think you made a tiny mistake: you want to multiply frequency and wavelength to get velocity instead of dividing. cm * MHz = cm per 1,000,000 s. This is the velocity that you compare to the speed of light.

Best wishes,
Amanda