Waves and Optics

It’s been a little while since CLEO and my last post. Things have been hectic to say the least. The past few weeks included:

  • a trip to Forest Grove to look for houses
  • a week at home with Carter (17 mo. old) while Leslie went to Volleyball tournament
  • showing our house twice
  • receiving two offers on our house
  • signing one of them

We’ve had the home inspection and are waiting on the “Requested Repairs” paperwork, otherwise things are looking good.

“What does this have to do with Waves and Optics?” you ask. Well that is the course that I am responsible for this fall. I’m also teaching Geometrical Optics I and Workshop Physics (calc-based intro) but those courses are already put together.

Waves and Optics with Prof. Dawes (aka PHY 332)… what will it be, what wonders of physics will be explored and experienced by students in my class? I am leaning towards using H. J. Pain’s “The Physics of Vibrations and Waves” which starts with simple harmonic motion, builds on the wave equation from SHM, and then branches out to sound, water, and EM waves. The latter parts of the book are primarily optics: diffraction, interference, scattering etc. I really want to work in some current research results, especially since things like slow- and fast-light naturally come out of a discussion of wave physics. Another neat topic in the news lately are negative-index metamaterials. Of course there are also my own research interests: pattern formation, and nonlinear optics.

I don’t think I’ll have trouble coming up with current material, but I’m happy to hear other suggestions on recent topics that would fit into a course on waves and optics. I’m sure there are plenty that I’m not thinking of at the moment. Especially welcome are suggestions from any of you experts outside my subfield of optics.

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4 thoughts on “Waves and Optics

  1. Is this more of an optics course? I am not an expert, but I see that college courses don’t have much of classical physics, something along the lines of “Theory of Sound”. In particular, I haven’t seen any non-mathematical (physics based) justification for the “end effect” in pipes.

    Reply
  2. Yes, it tends toward optics, mostly by virtue of the large number of wave phenomena that optics can demonstrate. Based on the older set of notes I have (from the version that was taught in 2003-4), the first few weeks included some sound waves and other types of waves. The second half of the course is entirely optics: polarization, interference, diffraction, reflection, refraction, etc. The final weeks covered optical systems and devices, lasers, and current topics.
    As to your question about the “end effect” perhaps it is understandable from the perspective of an air molecule. Recall that sound waves are regions of high and low density: compression and rarefaction, respectively. From the perspective of an air molecule, this means that as a sound wave goes by, you first get pulled one way, and then you get pushed the other way (as opposed to a water wave where you would get pushed up and then slide down). Imagine the group of air molecules that lives at the closed end of a pipe. They hit the wall if they try to go one way, so the only way that a standing wave can be established is if those molecules are at a node: the point in the standing wave that does not oscillate. That way the end molecules simply stay put. Conversely, since an open-ended pipe does not have the barrier, the molecules at the end are free to oscillate and so that is what they do.Some of the confusion arises when drawing a standing wave in a pipe. Typically people draw a wavy string-like line inside the tube. This isn’t how the molecules vibrate, this is more like a plot of the density at each point in the tube (for one instant in time).Let me know if that helped or hurt your picture of the end effect đŸ™‚

    Reply
  3. Thanks for the reply. What I am looking for is why the end effect is proportional to the diameter of the pipe. I have seen explanations based on the impedance on both sides, but that is perhaps overkill for this application. I used to explain it as waves radiating out in a hemisphere from the pipe, but now I am not so convinced. As to your explanation, my question would be why molecules vibrate at a small distance away from the end rather than _at_ the end of the pipe.

    Reply
  4. Ok, sorry for the misunderstanding. The end effect you refer to can be described via impedance, or also by a reflection that is 180 degrees out of phase. I like the animations shown here:

    http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html

    In particular, the pulses traveling in partially-open and fully-open pipes. The diffusion of the pressure wave as it exits, leaves the inverse wave to propagate back down the pipe. This also explains why the reflection occurs slightly past the end… and also why diameter matters. When the pipe is larger, the diffusion takes place over a longer length scale (the constant between the extra length and diameter is something like 0.6).

    Reply

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