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The vibration of a piano string is governed by the wave equation $u_{tt} - c^2u_{xx} = 0$ where $c$ is related to the tension and the mass density. Suppose a string is hit by a hammer on the interval $(-a,a) \subset \mathbb{R}$ where $a > 0$. A flea sits at a point $l>0$ where $l>a$. How long does it take for the disturbance to reach the flea?

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What are your thoughts? What have you tried so far? – Rahul May 24 '12 at 17:15
Keyword: finite speed of propagation. – Giuseppe Negro May 24 '12 at 17:21

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