An infinite string vibrates according to the homogenenous wave equation [tex] u_{tt}-u_{xx} = 0 [/tex] with initial data given by [tex] u(x, 0) =f(x) [/tex] and [tex] u_{t}(x, 0) = g(x) [/tex] for -infinity<x<infinity where both f and g are smooth functions that are positive on the intervals -4<x<-3 and 2<x<3 and both zero everywhere else along the x-axis. A person stands at location x=0.(adsbygoogle = window.adsbygoogle || []).push({});

The question is during what intervals of time will the person notice the string vibrating? I know the interval is t=x to t=infinity but what is the process of getting x? Sorry if this is a stupid question.

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# Vibrations and the wave equation

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