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The PDE.

  The PDE governing the transverse displacement u of the string is the wave equation  
 \begin{displaymath}
 \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2},\end{displaymath} (10)
where c2 is the ratio of the tension force in the string over its mass per unit length. This equation also governs other processes, such as the acoustics in a pipe and steady supersonic flow around thin wings. Like the one-way wave equation, it is an hyperbolic PDE.


Next: The boundary conditions. Up: The wave equation. Previous: The wave equation.