The reasonableness of vibration equation being used to solve wave equation

The solution of longitudinal wave of a column through vibration equation taken as an example, the vibration equation was proved to converge to wave equation when the discrete spatial size converges to be infinitesimal. Concept of calculation wave velocity was proposed. Wave´s propagation could be seen in the vibration´s solution obtained with central difference method when calculation wave velocity equal to physical wave velocity. The physical meaning of stability requirement of central difference method was revealed, that is, calculation wave velocity must be equal to or greater than physical wave velocity.