Solving the Wave Equation - Partial Differential Equations | Lecture 20

In this lecture we solve the wave equation with Dirichlet (pinned) boundary conditions. We use separation of variables to obtain a Fourier sine series representation of the solution, much like for the heat equation. The major difference is that we now find oscillations in time, as opposed to the exponential decay of heat flow. We focus on the physical interpretation of the solution, particularly applying it to the vibration of strings on musical instruments. We show how sound can be altered by changing the string length, tension, or material.

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[FaTeAnimationVault]

Beautiful presentation.
Affine space is my favorite kind of space.