Waves

October 17, 2006 10:15 PM

Recommendations for good explanations of waves and vibrations. I'm taking a college-level course (includes DiffEQ and some linear algebra) on the physics of waves, and it's completely stumping me. I need help parsing the topic as a whole. Much

Waves do not seem to offer the simplified generalizations that come so easily to classical mechanics, electricity and magnetism, and special relativity. I understand the derivations for the formulas and solutions for damped harmonic motion, forced harmonic motion, finding the quality factor, etc, but it doesn't all make sense, and therefore I can't apply it to real-world problems.

I'm not sure how to explain this. With the other physics topics I've mentioned, I can see the big picture and apply the formulas to real-world problems and understand how and why I'm using that formula over another one. With waves, I don't see any overall picture, just a bunch of seemingly ridiculously over-complicated formulae that only barely fit together. I don't know if this is just how waves is or whether it's the presentation. Right now I've gone through HRK, Feynman's Lectures, and Pain. Can anyone point me to other oresources or techniques they found especially useful?

posted by schroedinger to education (12 comments total)

French is my standard quick reference for this stuff, and it seems like a perennial favorite. It's succinct and clear.
posted by mr_roboto at 10:27 PM on October 17, 2006

you might want to check this out from the MIT opencourseware

but you are right, wave mechanics is not as well covered as other physics courses in general. My suggestion is to go to a bookstore and peruse books on this, you will find some that are better for your level and others which are too difficult. Pick a few in a library. Also your profs should be able to guide you. Profs love to be asked to give out other material.
Wave theory is a very interesting field, vibrations, strings, electromagnetism. Keep at it.
posted by carmina at 10:35 PM on October 17, 2006

By diff eq, I'm assuming only Homogenous and Non-Homogenous ODEs?
posted by Loto at 10:36 PM on October 17, 2006

Correct, Loto.
posted by schroedinger at 10:50 PM on October 17, 2006

I highly reccomend Waves: Berkeley Physics Course, Vol. 3 by Frank Crawford. It's out of print, but I'm sure you can find it in a college library.
posted by funkbrain at 11:04 PM on October 17, 2006

I second Crawford, and note that if you want a copy for yourself, Caltech got permission to make reprinted, spiral-bound copies for their fall sophomore waves class--call them and ask to get their Ph12a book. Or, it looks like Amazon has a couple copies, used.
posted by Upton O'Good at 11:35 PM on October 17, 2006

I think it's the presentation. First off, many wave problems aren't physically directly related - it merely happens that, while the nature of the forces involved are unrelated, they have similar effects, particularly when it comes down to modelling the situation mathematically. So in some sense there isn't necessarily some big overall picture you should be trying to see. You're being taught how to deal with a set of similar but often unrelated problems, and some aspects of the techniques will be more obvious and more useful in some problems than in others.

Second, is there any form of experiment involved in your lessons? I didn't really get to grips with how some things (including certain wave problems) worked until I sat down and applied it to a system that was actually in front of me and that I could examine, prod and poke. I'm not saying I'd never have managed to get on top of it without that, but it got me there a lot faster and left me a lot better placed to apply stuff to problems on paper.
posted by edd at 1:22 AM on October 18, 2006

One of the things that tied waves together for me is their application in music and musical instruments. Maybe having that as a concrete model will help. This textbook (and you can tell it's a text book by the extortionist price) has some pretty good explanations of what's happeneing in sound waves. If your college library doesn't have it, I bet they could get it on loan.
posted by plinth at 5:32 AM on October 18, 2006

I've always been good at physics and electronics (... except for a lifelong problem with differential equations)

I "got" waves through:
- highschool demonstrations with ripple tanks
- basic sound and music material
- radio theory
- electronics and oscilloscopes
- understanding the cycle of a sine wave is like the motion (in one axis) of a point on the circumference of a rotating wheel
- an overdose of great science museums (best is Ontario Science Centre, Toronto) that had many great demonstrations of waves - strings, oscillators, ripple tanks, etc

Like most people you may "get" it best though observing it in application, rather than fighting with theory. I don't know what your ultimate application for wave theory is, so i can't suggest an appropriate example, but for me in electronics and engineering, appropriate examples are
- resonant filters
- reflections in transmission lines
- radio tuning
- AC power transmission
posted by Artful Codger at 7:39 AM on October 18, 2006

Rotation and linearity.

There are only a few general trends possible: stay the same, grow, shrink, and oscillate. You can also have combinations of those, of course, like an exponential increasing function with a small oscillation superimposed.

It is hard to deal with the abstract notion of trends in general, but if you constrain the problem by assuming linearity, you can actually start doing closed form math. Anything that oscillates linearly is sinusoidal, and all the standard wave techniques apply.

It gets really astonishing when you realise that assuming linearity implies that all of the possible trends for any variable can be mathematically represented with the complex exponential - linear algebra, eigenvalues, systems & signal analysis, information theory..

So, exactly as edd has said, the physical effects involved are different, but they are tied together because waves are rotating.
posted by Chuckles at 8:33 AM on October 18, 2006

Crawford really can't be bettered as far as I know, and it has tons of examples, too (and the early editions had a great little kit of polarizers, diffraction gratings, etc. for all the experiments he recommends), but it's kind of a difficult book in its own right despite spare use of formulas, in my opinion, though quite worthwhile.

J. R. Pierce's Almost All About Waves, as I (somewhat dimly) recall, attempts to push intuition as far into the advanced reaches of the subject as it can possibly go, with considerable success.
posted by jamjam at 10:54 AM on October 18, 2006

Well, the problems you are doing now are no doubt highly simplified, but the one thing to remember is that Hooke's Law is actually very applicable in the real world. Things bobbing in water and the like. Since you mentioned a quality factor, you have probably dealt with resonance. Think of pushing someone on a swing such that each push sends them higher and higher. Look for an engineering text in your library, that will most likely have more of what you need. Kreyszig's Advanced Engineering Mathematics is good.

The other thing to remember is that the meat of real world applications come in the form of partial differential equations.
posted by Loto at 3:28 PM on October 18, 2006