 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/20/a/solution

Yes. The wave equation is linear and homogeneous. For

W = \partial_{x}^{2} - c^{- 2} \partial_{t}^{2}

A, B

W (A f_{1} + B f_{2}) = A W f_{1} + B W f_{2} .

If both terms on the right vanish, their combination is also a solution. Thus the superposition principle applies, and it also preserves homogeneous fixed-end boundary conditions.

 New to topics? Read the docs here!