Wave Propagation solution for a variable area 1D duct

  1. In the problem I am suppose to use the wave equation to solve it.

    I assume 1D plane wave duct,

    u(x,t) = 1/(rho*C)*real((Aexp(ikx)-Bexp(-ikx))exp(iwt))
    where C is the speed of sound, u is the velocity, p is the pressure, w is the angular frequency, t is time, rho is the density, and both A and B are unknown constants which I have to find.

    The equation for Pressure is similar except without density and speed of sound term,
    p(x,t) = real((Aexp(ikx)-Bexp(-ikx))exp(iwt))

    At the area changing point, I am suppose to assume the same pressure and Aa*U1 = Ab*U2 (essentially matching the conditions)

    After applying the left end B.C, I get A = B
    But I can't move any further.... Any help would be greatly appreciated.

    Attached Files:

  2. jcsd
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