# D'Alembert's solution for the one-dimensional wave equation for a semi-infinite string

Find the solution to:

PDE: u*xx-c(to the power of negative k)u*tt=0 , 0

ICs: u(x,0)=f(x) and u*t(x,0)=g(x), x>=0

BC: u*x(0,t)=0 , t>=0

This BC corresponds to a string with its end point free to move in a vertical direction.

(Please remember to include to boundary condition in your solution. Thanks very much!)

Hello! Thank you for taking the time to try and solve this problem. Please note that I am unable to use math symbols. Thus, I will use * to symbolize a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. Here is the problem: (also note that the PDE is the one-dimensional wave equation)

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#### Solution Summary

D'Alembert's solution for the one-dimensional wave equation for a semi-infinite string is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.