1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

D'alembert solution for the semi-infinite string

  1. Nov 18, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the solution of the wave equation using d'Alembert solution.

    2. Relevant equations
    and [itex]u(x,0)=0[/itex]
    [tex]u_t(x,0)=\frac{x^2}{1+x^3}, \, x\geq0[/tex]
    [tex]u_t(x,0)=0, \, x<0[/tex]

    3. The attempt at a solution
    For a semi infinite string we have the solution
    [tex]u(x,t)=\frac{1}{2}\left( a(x-ct)+a(x+ct)-a(-x-ct)-a(-x+ct) \right)+\frac{1}{2c}\left( \int^{x+ct}_{x-ct} dy\, b(y) - \int^{-x+ct}_{-x-ct} dy\, b(y) \right)[/tex]
    with [itex]u(x,0)=a(x)=0[/itex] so
    [tex]u(x,t)=\frac{1}{2c}\left( \int^{x+ct}_{x-ct} dy\, b(y) - \int^{-x+ct}_{-x-ct} dy\, b(y) \right)[/tex]


    Is this right?
    Last edited: Nov 18, 2014
  2. jcsd
  3. Nov 23, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Jan 2, 2015 #3
    Thsi is what I came up with
    for [tex]x \geq ct[/tex]
    and [tex]x < ct[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: D'alembert solution for the semi-infinite string
  1. D'Alemberts Solution (Replies: 1)