Discussion
Consider the following statements about the wave equation. 1. Its general solution is a sum of two travelling waves 2. It is hyperbolic 3. A single travelling wave can satisfy both initial conditions
Answer: A
The first two hold. The third fails: two initial conditions, the initial displacement and the initial velocity, need two arbitrary functions to satisfy, so one travelling wave is not enough unless the two conditions happen to be compatible with it. That is exactly why d'Alembert's solution carries both terms
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