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Using the d'Alembert operator for wave equations

  1. Dec 21, 2008 #1
    1. Is there anywhere where I can find a derivation for the generalized inhomogeneous wave equation? I found a derivation of the 1D wave equation for an infinitesimal region of an elastic string here:

    http://www.math.ubc.ca/~feldman/apps/wave.pdf

    But I am looking for proof of the generalized version in n dimensions where
    [(grad)^2-(1/c^2)d^2/dt^2)]f=0 in free space.

    Additionally, I'm having trouble following this derivation of the solution to the time-dependent Green's function here:
    http://farside.ph.utexas.edu/teaching/em/lectures/node49.html

    I can understand the derivation of the generalized solution to Poisson's equation in the time-independent case, but I'm having trouble understanding lines 487-492 in the link above. Intuitively, I can understand where the solution comes from since an observer at r will only measure the potential resulting from an impulse at t' and r' at time t=t'+(/r-r'//c), so we use the delta-dirac function, and the potential still falls off like 1/r so the spatial component is the same as the time-independent case. Can anyone help with those lines?
     
  2. jcsd
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