# Wave Equation : D'Alembert's Solution

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See the attached file.

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

and

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.

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#### 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 solution to a wave equation is investigated and the details are presented.

$2.49