(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An infinite string obeys the wave equation (d2z/dx2)=(ρ/T)(d2z/dt2) where z is the transverse displacement, and T and ρ are the tension and the linear density of the string. What is the velocity of transverse travelling waves on the string?

The string has an initial displacement

z= (h/L)(L-x) for 0<x<L, (h/L)(L+x) for -L<x<0, 0 otherwise

where h is a constant. The string is initially at rest. Sketch z(x,t) at the times

t=αL√(ρ/T) for α=0, 1/4, 1/2, and 1.

2. Relevant equations

3. The attempt at a solution

v=√(T/ρ), from the wave equation.

Using D'Alembert's solution, I get z=(h/2L)(L-(x+ct))+(h/2L)(L-(x-ct)) for 0<x<L

and z=(h/2L)(L+(x+ct))+(h/2L)(L+(x-ct)) for -L<x<0 and 0 otherwise.

But the ct terms seem to cancel, so I'm guessing I've gone wrong somewhere. :-/

Thanks in advance for any help! :-)

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# Homework Help: Sketching wave equation solutions.

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