The problem I have is in acoustic guitar design, for simplicity imagine a box 20"X15"X3" (length, width, depth). On one of the 20X15 surfaces (the top) cut a 3" hold 1/3 from one end centered along the major axis. On the same surface place a vibration generator to drive the surface (generate sound) also centered along the major axis approximately 1/3 from the opposite end. Assume all the other sides and back of the box are infinitely rigid perfect reflectors.

Now assume the second 20X15 (the back), although being perfectly ridged can be deformed to any desired shape and then frozen in that new shape for the ray tracing analysis. What is the optimum shape of the back to focus as much sound as possible out of the box through the hole?

Now change the shape of the sides from a box to a guitar body and repeat the analysis to make fine adjustments to the curvature of the back. I'm assuming this optimum shape of the back would be some variation on a parabolic dish, but a deformed parabolic dish considering the shape of the guitar outline and the fact that the acoustic driver and the sound hole are off center.

Is this optimization algorithm something a standard ray tracing package can do? Can it (the ray tracing software) optimize the back shape within a certain set of predefined parameters. I'm assuming this problem is similar to solving a ray trace analysis for designing a mirror. If not, are there any better methods that anyone can recommend to solve this problem?

Thank you,

Steven