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Wave Equation : D'Alembert's Solution

Given that the general solution to the wave equation in one space dimension

is given by

where f, g are arbitrary twice continuously differentiable functions deduce that the solution s satisfying the initial conditions


for some function v, is

(this is a special case of the so called D'Alembert's solution of the wave equation).

Please see the attached file for the fully formatted problem.


Solution Preview

Take the partial derivative of this equation with respect to x holding t constant

The integral is (1/2c) [F(x+ct) -F(x-ct)] = ...

Solution Summary

A olution to a wave equation is investigated.