ABSTRACT
The propagation of a wave in 1-d, ψ(t, x), is governed by local dynamics in which the instantaneous acceleration depends on the local curvature of the wave form, i.e.,
a ∝ ∂ 2ψ
∂x2 .
Identifying the acceleration as a = ∂ 2ψ ∂t2 , and realising that the wave speed [squared] is the
sole dimensional parameter extant which can fulfill the roˆle of proportionality constant, one obtains the canonical form of the wave equation:
0 = ∂2 ψ
∂x2 − 1 c2
∂2 ψ
∂t2 .
