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