d’Alembert’s wave equation

D'Alembert's wave equation, formulated as (y_{tt} = c^2 y_{xx}), describes the motion of waves, such as those on a vibrating string. This partial differential equation relates the acceleration of a string segment ((y_{tt})) to its tension ((y_{xx})).1

The equation's general solution, (y(x, t) = f(x + ct) + g(x - ct)), represents two waves traveling in opposite directions. This mathematical framework is fundamental in understanding various wave phenomena in physics, including sound and light.12