Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving the Wave Equation in semi-infinite domain with easy ICs

  1. Mar 25, 2013 #1
    Hi, so the problem is this:

    I am trying to solve (analytically) the wave equation with c=1:

    [tex]u_{xx}=u_{tt}[/tex]

    on x,t>0 given the initial conditions

    [tex]u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt)[/tex]

    I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms, D'Alembert's solution and separation of variables. But I keep getting u=0 with these familiar methods due to the initial conditions of u being 0 and unmoving at t=0.

    I feel like this is easier than I'm making it! Anyway, any help would be appreciated!
     
    Last edited: Mar 25, 2013
  2. jcsd
  3. Mar 25, 2013 #2
    Yeh... After solving numerically I realised that I just hadn't thought about the fact that the waves must propagate at speed 1 and u=0 for all x>t. So a quick bit of algebra gives:

    [tex]u(x,t)=H(t-x)sin(w(t-x))[/tex]

    simples
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving the Wave Equation in semi-infinite domain with easy ICs
Loading...