Waves in Several Dimensions - Chladni's Method

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Contents 1 Slide 3 2 Slide 4 3 Slide 5 4 Slide 6 5 Slide 7 6 Slide 8 7 Slide 9

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Slide 3

Graph of psi from Erwin meets Goldilocks. High energy can be viewed as more curvature (greater d(psi)2/dx2) or an increase in the number of nodes (where the graph crosses not just touch zero). [edit]

Slide 4

Different psi graphs for a double minimum potential. Erwin meets Goldilocks can handle complicated 2-dimensional tracing. [edit]

Slide 5

Yet, Erwin meets Goldilocks only works for 2-dimensional tracing! With more than one dimension it is not clear how much of the total curvature to assign to each dimension, so it is impossible to continue curves as is done in Erwin Meets Goldilocks. [edit]

Slide 6

Chladni's Acoustics. Introduction to treatment of an analogous wave problem more than a century before Schrödinger. [edit]

Slide 7

Chladni's method. He suspended a plate, put sand on it, and bowed it. By touching different parts of the plate, he got different patterns of sand. [edit]

Slide 8

Short movie of Chladni. [edit]

Slide 9

Some Chladni figures. Note that where the sand collects are the nodes i.e. where the plate doesn't move/vibrate. Nodes form either as diameters or circles.