# Vibrations and the wave equation

1. Oct 2, 2005

### Tony11235

An infinite string vibrates according to the homogenenous wave equation $$u_{tt}-u_{xx} = 0$$ with initial data given by $$u(x, 0) =f(x)$$ and $$u_{t}(x, 0) = g(x)$$ 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.

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.