English: To obtain the wave equation from File:Force on lumped mass for string waves.svg we note that the displacements from the equilibrium points ${\displaystyle \psi _{j}}$ (top of figure) play no direct role in calculating the forces. Instead the force on any given mass depends on the difference between consecutive displacements. For any function ${\displaystyle f(X)}$, we identify the difference with a derivative and use the prime notation. For example
${\displaystyle f^{\prime }(X)\approx {\frac {f(X+h/2)-f(X-h/2)}{h}}}$