Ideal String Wave Equation

For definiteness, let's consider simulating the ideal vibrating string, as shown in Fig. 1.

Figure 1: The ideal vibrating string.

The wave equation for the ideal (lossless, linear, flexible) vibrating string depicted in Fig. 1 is given by

$$Ky''= \epsilon {\ddot y} \protect$$ (1)

where

$$\begin{array}{rclrcl} K & \isdef & \mbox{string tension} & \q... ...isdef & \frac{\partial}{\partial x}y(t,x) \nonumber \end{array}$$

and ``$\isdef$'' means ``is defined as.'' The wave equation is derived, e.g., in [19].