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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}](img20.gif) |
(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.