The PDE.

  The PDE governing the transverse displacement u of the string is the wave equation  

$$\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2},$$ (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.