text: Given that we saw that
  If we make the previous assumptions of the fluid being ideal and the velocity being irrotational, then we have
  Under these assumptions, our linearized sound equations become
  Importantly, since  is a constant, we have , and then the second equation tells us that
  Or just that
  Now, when we use this relation with the fact that , alongside cancelling and rearranging terms, we arrive at
  We can write this in a familiar form as
  This differential equation must be solved with the appropriate boundary conditions. Note that setting  returns us the wave equation. Regardless, upon solving this equation for a moving medium, we then have