## Chapter 19WAVES IN ONE DIMENSION AND WAVES WITH SPHERICAL SYMMETRY

### 19·01. Vibrating string: d’Alembert’s solution.

In a large class of physical problems we meet with the differential equation

where *t* is the time, *x* the distance from a fixed point or a fixed plane, and *c* is a known velocity. The general solution of this equation was given by d’Alembert. We take as new variables

and then by transforming the differential equation we get

It follows ...