Reading assignment: PpP 3.1-3.5; 17.1,17.2
Boy, math-heavy reading for today!
But this discussion is a model for one of those (many different) skills that you need to foster as a physicist (or an engineer, or physical scientist)---the skill of coming up with a guess, trying it out, figuring out why you have to reject it, and then coming up with another guess that is only slightly more complicated, and then continuing the loop until you get something that works.
What was wrong with the first solution that was tried in the reading today (PpP
section 3.2)? What assumption did it start with and how could Dr. Durfee tell
that that assumption
The starting point assumed that there was one incoming wave and one transmitted wave, and the the transmitted wave had a new velocity. Dr. Durfee could tell that the assumption was wrong because the second boundary condition--slope of wave shape is same on left as on right--required (given that guess) that the wave number not change. But that would mean the velocity doesn't change, so there's a contradiction.
How did the next guess (section 3.3) build on the first?
The second guess allowed for a reflected wave. Not only does this match experiment (see the demos in class today) but the math works out now.
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