Got an e-mail about a guy who teaches physics and has a way of calculating the speed of light from a common event. Heats up a wide layer of marshmallows in a microwave. Notices that there are spots of overdone marshmallows in the dish. Sees they’re all about 6cm apart and says, that’s 1/2 the wave length of the micro waves in the oven. Now, simply multiply that by the frequency, as indicated on a panel on the back of the microwave oven, and you have the velocity. Wave length x frequency = velocity. Fair enough, except how does he jump to the conclusion that the 6cm represents 1/2 of the wave length? If I understood that, I’d think this was more useful in a classroom. Any help?
Each spot represents a point of maximum intensity, which is either a peak or a trough on the waveform. Peaks and troughs are 1/2 wave apart.
If you want to do the math yourself, the frequency of a consumer microwave oven is 2.45 GHz or 2450 MHz.
In case that wasn’t clear, have a look at this diagram. The wavelength is the distance between adjacent peaks (crests in the diagram). Peaks represent maximum intensity in one direction, while troughs represent maximum intensity in the other; somewhere in the middle (like this) is a line which represnets zero intensity.
Almost tempted to open a new thread, but anyway…
I wonder what the best arrangement of food in the microwave should be to ensure even
cooking with a minimum of cold spots (I have a turntable inside). Should I put it smack dab
in the middle and let it turn, or offset it as far as I can from the center, or something in
between?
Doesn’t that assume a standing wave? Are oven dimensions tuned to provide standing waves?
Yes, there are standing wave patterns inside the oven cavity.
No, not exactly. There will always be a standing wave pattern inside the cavity, which will vary depending not only on the dimensions and geometry of the cavity, but also what’s in it. Just like light slows down travelling through various media in varying amounts depending on the refractive index, microwaves travel at different speeds through different materials and this, in turn, will alter the standing waves. In any case, the cavity need not be of any particular dimensions to create a standing wave pattern, but if it’s rectangular in shape, the wave pattern will be simpler and more ordered.
So just to be clear QED are you saying this is a legitimate experiment to measure the speed if light?
I’m not making the argument that is not legitimate, I just think it’s really cool if it actually works.
Well, it’s not going to be anything like accurate if that’s what you mean; if you can get an answer to within 10% of the actual value for c, I’d be impressed. But on the whole, I’d say it’s a useful classroom demonstration of how such problems could be solved, yes.
The basic underlying principle is sound. But things like uncertainties in measuring between the exact centers of the spots and the standing wave pattern not being oriented squarely with the sides of the cavities will tend to make your final result less than accurate. As will the fact that air inside the cavity will slow down your microwave photons a bit. And, complexities in the wave pattern can easily make locating hot spots corresponding to adjacent peaks and troughs difficult, if not impossible.
It’s perfectly legitimate, though you won’t get a high degree of accuracy.
My science teacher did this experiment for us back in 7th grade. He used a puddle of melted chocolate instead of marshmallows, though.
For me, there’s still a leap. Several. I don’t know enough about waves to argue, but it doesn’t seem automatic that the maximum intensity of a wave is at the peak. I’m not even sure what maximum intensity actually means in this context. But water waves appear to have enough energy to lift a floating cork at every place on the wave, if that’s an apt analogy. On the other hand, I do know that if I’m standing in shallow water, I’m most likely to be knocked down when the peak of a wave strikes me. Is that more apt? And, even if that were so, why would I assume that the soft spots correlate with that fact? Off hand, I’d guess that there could be a number of reasons that there was greater heating in regularly spaced spots, including some sort of reinforcing resonnance or interference of any number of waves of any number of wavelengths. Can I get some more help here?
Both analogies are apt; when the cork is atop the peak of a wave, it has more potential energy than when it is at the midpoint.
Try this: A floating cork is furthest from its mean value on the tops of the crests and the bottoms of the troughs.
It is exactly “some sort of reinforcing resonnance or interference”. And whenever you have that, the spots that reinforce are half a wavelength apart.
Arrange the food into a donut shape if possible. Try to make the hole at least 6 cm (1/2 wavelength) across, and keep the sides of the donut itself no bigger than 6 cm across. I’ve had good results doing this.
Using the numbers provided by the OP and Q.E.D.:
Wavelength=26 cm=.12 m
Frequency of waves=2.450 GHz
.12 m2.45010^9 GHz=2.9410^8 m/s
One significant figure provided by OP (which would actually make it more accurate, which is why I’m not doing it that way):
|294000000 m/s - 299792458 m/s|/299792458 m/s=1.9% error.
Either this is a much more reliable definition than you thought, or one of these data don’t match up.
Well, that’s already assuming a measurement of very close to the actual 1/2 wave of consumer microwave ovens (6.1 cm). I don’t know as that’s the actual measurement that was taken; the OP says “about 6 cm”.
Let’s be real careful of terminology here. This is a classroom activity (NOT experiment), in which students are helped to calculate the speed of light from some data which is provided. There is no measurement of the speed of light here. It’s pretty interesting, and with enough background information - such as some which has been provided here by** Q.E.D.** - it would be a nice demonstration. It is most definitely not a legitimate experiment of anything, least of all the measurement of the speed of light. Illustration, yes. Demonstration, yes. Activity, yes. Experiment, no. Measurement of the speed of light, no.