The fundamental result of Fourier analysis is that we are saying the same thing :) Though I should have clarified that the kinetic energy is zero at the "boundary" (ie bridge).
IMO which answer you prefer depends on perspective:
- if you assume a wave can be broken down into sinusoidal overtones then your geometric approach is much more immediate and intuitive: sinusoidal overtones => higher overtones clearly have more kinetic energy near the boundary, just draw a picture.
- if you assume that higher-pitched overtones have more kinetic energy then the physics approach explains why they are sinusoidal. Not the specific shape unless you do the math, but the "gist" of the slope. If the overtones were more like square waves, with no real difference in shape between frequencies beyond the length of the rectangle, then the pickup position wouldn't matter. But they can't be, the overtones have to be more "trapezoidal." And in particular, the lower overtones must have a more gradual slope than the higher overtones.
The geometric approach makes a big (but correct) physical assumption for an easy analytical argument; the physical approach goes the other way, only depending on Newton's laws + a lot of elbow grease.
