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The wave equation.

The next of the fundamental PDEs governs the transverse vibrations of a string as shown in figure 9. During the vibrations, kinetic energy due to the transverse motion of the string is converted into potential energy in the string and vice-versa. Friction is ignored.

**Figure 9:** Vibrations of a string.
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The PDE.
The boundary conditions.
The initial conditions.
The general solution.
Smoothness of the solution.
Characteristic lines.
The domain and numerical solution.

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