The 1-D wave equation

Taking the limit as $\Delta x \longrightarrow 0$

$$\lim_{\Delta x\rightarrow 0}\frac{\Delta \mbox{m}}{\Delta x} = \frac{\partial \mbox{m}}{\partial x} = \frac{\partial^2 y}{\partial x^2},$$

we obtain the one-dimensional wave equation given by

$$\frac{\partial^2 y}{\partial t^2} = c^2\frac{\partial^2 y}{\partial x^2},$$

where $c = \sqrt{T/\mu}$ is the speed of wave propagation.