The mathematics of PDEs and the wave equation

to the curvature at the point, as indicated in the figure. Then mass times acceleration ρu tt should equal that force, ku xx. Thus u tt = c2u xx where c = p k/ρ turns out to be the velocity of propagation. Figure 1: The restoring forces on a vibrating string, proportional to curvature. Let’s do it again, from an action integral.

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