Solve the two-way wave equation

Consider the two-way wave equation

$u_{tt} − u_{xx} = 0$

for $t ≥ 0$ and $x ≥ 0$ with initial data $u(x, 0) = u_0(x)$ and $u_t(x, 0) = 0$ for $x ≥ 0$ and boundary data $u_x(0, t) = 0$ for $t > 0$

Draw a diagram of the problem in the $x − t$ plane.
Solve the problem in terms of $u_0$. Describe the interaction of the left-moving wave with the $x = 0$ boundary (one sentence).


Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer

1 Attachment

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.