[Klaynos]

swansont said:

It's good — anything to within 10% is for something like this — but it's not the error. Unfortunately this is often taught in physics class, or at least is not corrected. Error has to do with uncertainty concerning the experiment, not the difference between your answer and the accepted one. You might estimate that your measurement of the wavelength is to within ±0.5 cm. which would be ± 1.2e7 m/s, or 7.7% error. In that case, your answer and the accepted on agree to better than the error. Alternately, (and more deliciously) you could do the experiment many times and find the standard deviation of the measurements.

I was also going to post this when I commented on wondering the refractive index of chocolate, and whether it matters due to the amount of wave in the air compared to the chocolate...

[hermanntrude]

mooeypoo said:

That's a good point, I didn't think about that..

But to change the percentage you need relatively large changes in the speed between the air and the chocolate -- the wave, after all, traveled about an inch in chocolate, probably even less --- does that really make that much difference in terms of the speed?

The speed of light is related somehow (not sure exactly how) to the density of the medium. The speed of light in water is about 2.2 (i think?) x 10^8 m/s, and since chocolate has a density much closer to that of water than that of air or vaccuum, we might expect the value to be in the mid to low 2's rather than 3, although there is further complication in that the wave probably doesn't travel entirely through chocolate

swansont said:

———

I don't agree that you should use the speed of light in chocolate. The standing wave is in the air. The wave in the chocolate would not generally be a standing wave, it will be two traveling waves, and will not give you nodes and antinodes, since the return wave will be out of phase. And the amount of power in that wave will be small.

that sounds interesting. However, your predictions defy my limited knowledge of wave mechanics. If you are right, hopefully the albumin adaptation will help to prove it.

[Klaynos]

hermanntrude said:

The speed of light is related somehow (not sure exactly how) to the density of the medium. The speed of light in water is about 2.2 (i think?) x 10^8 m/s, and since chocolate has a density much closer to that of water than that of air or vaccuum, we might expect the value to be in the mid to low 2's rather than 3, although there is further complication in that the wave probably doesn't travel entirely through chocolate.

It's far more complicated than just density being important. But it can be simplified into refractive index, which is the ratio of the speed of light in a vacuum / speed of light in a material. It's also wavelength dependent.

It is possible to work out the refractive index of a material, but unfortunately I don't have easy access to a microwave spectrometer at the moment. Give me a few months and when I start my studentship I'll ask one of my friends the feasibility of it, I suspect we'll need a 1m square of very flat chocolate though....

[swansont]

hermanntrude said:

that sounds interesting. However, your predictions defy my limited knowledge of wave mechanics. If you are right, hopefully the albumin adaptation will help to prove it.

Take a rope, tie it to a pole or tree, etc., i.e. something solid. Shake it to make a standing wave. Now, let the tips of it hit the ground. What happens to the wavelength? Does the position of the antinode(s) shift much? (the answer should be essentially nothing/no) You're driving the wave in a medium at a certain frequency, and that dictates the wavelength. Not the interaction with the ground, even though you are coupling some energy to it.

If the microwave were largely filled with chocolate, then your scenario would apply. That would be letting much of the standing wave hit the ground, rather than the tips.

[hermanntrude]

Klaynos said:

It's far more complicated than just density being important. But it can be simplified into refractive index, which is the ratio of the speed of light in a vacuum / speed of light in a material. It's also wavelength dependent.

I'm aware that it's more complicated than that, and unfortunately I have to teach my students annually about refractive indexes without going into any of the interesting details. Anyway Ijust thought that the density might give us a first approximation

swansont said:

Take a rope, tie it to a pole or tree, etc., i.e. something solid. Shake it to make a standing wave. Now, let the tips of it hit the ground. What happens to the wavelength? Does the position of the antinode(s) shift much? (the answer should be essentially nothing/no) You're driving the wave in a medium at a certain frequency, and that dictates the wavelength. Not the interaction with the ground, even though you are coupling some energy to it.

If the microwave were largely filled with chocolate, then your scenario would apply. That would be letting much of the standing wave hit the ground, rather than the tips.

well i guess we wont know until someone does the remake. Certainly it seems we have a good case for reducing the quantity of the test material to a minimum to reduce any changes in the speed of the waves to another minimum

[Klaynos]

Diamond:
Density 3.5-3.53 g/cm³

Graphite:
Density 2.09–2.23 g/cm³

The opaque one at visible frequencies is the least dense... I picked these two as they are both carbon... So I don't think we could even take a good guess at the refractive index of chocolate for microwaves :(

[hermanntrude]

Klaynos said:

Diamond:
Density 3.5-3.53 g/cm³

Graphite:
Density 2.09–2.23 g/cm³

The opaque one at visible frequencies is the least dense... I picked these two as they are both carbon... So I don't think we could even take a good guess at the refractive index of chocolate for microwaves :(

hmm... well it's written in the textbook i teach from (which was written by a self-important ignorant prick), that when light goes from a less dense to a more dense medium it is refracted away from the normal, because the speed of the light is lowered by different amounts, and vice versa.

I'd like to get to the bottom of this, since I have known this textbook to be wrong before, and I need to know where the wrong parts are

[Klaynos]

Another more common example:

Glass (fused silica):
2.203g/cm³
Refractive index: 1.459 at 589.29 nm

Water:
0.998g/cm³
Refractive index: 1.33393. at the same wavelength

So here less dense lower refractive index holds, this seems to be where the problem occurs.

Also you get things like if you add salt to water the refractive index goes up.

So it is often taught that refractive index is bassed highly on density, but it's only really because the situation that are often taught happen to be true... Most solids have a higher refractive index than liquids, but IIRC this is mostly to do with the bonds than anything else.

[swansont]

hermanntrude said:

hmm... well it's written in the textbook i teach from (which was written by a self-important ignorant prick), that when light goes from a less dense to a more dense medium it is refracted away from the normal, because the speed of the light is lowered by different amounts, and vice versa.

I'd like to get to the bottom of this, since I have known this textbook to be wrong before, and I need to know where the wrong parts are

It applies to a traveling wave, but it's bent toward the normal if the optical density is higher. It minimizes the time spend in the denser medium while also reaching its target.

[hermanntrude]

toward, yes. I still have to look that one up, and last night i was out of town