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.
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)] = ...
A olution to a wave equation is investigated.