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Homework Help: The propagation of disturbances in interstellar gases

  1. Nov 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that the solution of the form ρ1 = ρ1(x±a0t) satisfy the equation:

    2ρ1/∂t2 - a022ρ1/∂x2 = 0

    and that they correspond to waves propagating in the directions x increasing or decreasing.

    2. Relevant equations
    P = P0 + P1
    ρ = ρ0 + ρ1
    u = u1

    3. The attempt at a solution
    P1 = nKρ0n-1ρ1 ≡ nP00 * ρ1

    We shall define a quantity a02 = n * P00.
    a0 has dimensions of velocity and is a constant.

    The linearized form of the continuity equation is:
    1/ρ0 * ∂ρ1/∂t + ∂u1/∂x = 0

    The linearized form of the momentum equation is:
    ∂u1/∂t = -1/ρ0 * ∂P1/∂x

    This is as far as I have gotten with the problem. This problem can be found in the book of the physics of the interstellar medium by Dyson and Williams. Any help and I would be grateful!
  2. jcsd
  3. Nov 14, 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?
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