Chapter 18 · Partial Differential Equations
18.06
The Wave Equation
A vibrating string obeys u_tt = c²u_xx. Fixed ends give standing waves at whole-number harmonics; on an infinite string, d'Alembert's formula splits the start into two waves traveling apart.
About 17 minutes
You'll learn to
- →Derive the wave speed of a string
- →Solve the wave equation with fixed ends by separation of variables
- →Find harmonic frequencies
- →Use d'Alembert's formula