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I am trying to use frequency-wavenumber analysis to estimate sound wave propagation in a moving medium (fluid). I need to test the technique on analytical data. I wonder if there is an analytical solution that describes pressure field during sound wave propagation from a point source in a flowing fluid. I expect the pressure field to be a functin of space and time and it should show Doppler shift effect. I am assuming a simple problem with the following assumptions:

  • Fluid flow is one-dimensional.
  • Fluid motion is uniform.
  • Fluid is extending to infinity in both sides (i.e., boundary effects are negligible).
  • Sound source is a point-source (i.e., sound source does not affect fluid flow).

I am looking for 1D solution that can estimate acousic wave amplitude as function of space ($x$) and time ($t$). I think the solution should be identical to point source which is moving in a static fluid.

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  • $\begingroup$ See Problem 1, page 266, Chapter 68, Landau-Lifshitz, Fluid Mechanics, Vol 6. $\endgroup$
    – Navid
    Commented Oct 11, 2023 at 15:43
  • $\begingroup$ @Navid Thanks for your help. I think this not what I am looking for. I am looking for a solution of pressure wave from a point source in a moving medium. Pressure fluctuation is expected to be function of postion and time. It should clarifies Doppler shift effect. $\endgroup$
    – Signal Processing
    Commented Oct 12, 2023 at 19:04

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