lex,

Equations (11.74) and (11.75) show that the functional forms of F(x - ct) and G(x + ct) are identical to the functional forms specified in Eqs. (11.74) and (11.75) with x replaced by (x - ct) and (x + ct), respectively. Substituting these values into Eqs. (11.74) and (11.75), respectively, and substituting those results into Eq. (11.69) yields

I ( I J.X+C1 )j(x, t) = - ¢(x - ct) + ¢(x + ct) + - em d~ 2 2c x-cl

(11.76)

Equation (11.76) is the exact solution of the wave equation. It is generally called the D 'Alembert solution.