MATHS 361 Tutorial 5
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DEPARTMENT OF MATHEMATICS
MATHS 361
Tutorial 5
Solutions to the wave equation
1. Use separation of variables to solve the wave equation problem
(P DE) utt = a2uzz ,
(IC) u(x, 0) = f(x), ut (x, 0) = 0
for t > 0, 0 < x < L.
This is similar to our guitar string problem that we considered in class. As in the guitar string problem, the string is attached to the point (0, 0) (hence the BC u(0, t) = 0) . But this time the right end of the string can slide along a frictionless line x = L (hence uz (L, t) = 0) .
2. (Optional) Try running the matlab notebook (download from canvas) wave.mlx that plots solutions of the problem above, with a = L = 1. Several different initial conditions are given in the notebook.
3. How does this compare with d’Alembert’s solution? What kind of reflections occur at the boundaries?
2023-06-24