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
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.© BrainMass Inc. brainmass.com March 4, 2021, 6:18 pm ad1c9bdddf
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 solution to a wave equation is investigated and the details are presented.