Then, when you put your final, built horn into the world, you have to examine the effects of the world. That is where half-space, etc come into play. Now, the equation is no longer relevant.

I hope this makes sense.

I am not sure how programs such as Hornresp work, but, I suspect that they use an approximation method known as "finite elements." These approximate a solution of the wave equation, given simplifying assumptions and initial values. The initial values come from the assumed shape of the wavefront eminating from the horn and the presence of boundaries (walls, etc). This can be done relatively accurately in a controlled environment given sufficient computer power and financial resources.