We analyse a simple one dimensional arrangement of identical springs coupled with identical masses to understand longitudinal oscillations on the spring-mass chain. D'Alembert wave eqn implies only one wave-speed value, there is no wave dispersion. Ab initio analysis of the normal modes suggests that wave-speed in a closed-chain has dispersion. In the open-chain case, we can realistically associate a wave-length and wave-speed only for about half the normal mode solutions, because the higher frequency half of the modes on open-chains do not have sinusoidal solutions. In the normal mode analysis we find sinusoidal variation of frequency wrt mode number, not linear as expected by the idea of harmonics. Framing of D'Alembert wave equation is untenable. It is purely a geometric construct without any Physics basis to it.