Looking for ray tracing and surface optimization suggestions

[sdantonio]

I am a physicist who is interested in acoustic guitar design (additionally I make custom made guitars and violins).

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

 

[mmwave]

Dear Steven,

As a fellow physicist and acoustic guitar enthusiast, I find your question very intriguing. The optimization of the back shape in order to focus sound through the hole is indeed a complex problem, but it is one that can be solved using ray tracing analysis.

Firstly, I would like to confirm that your assumption of the optimum shape being a deformed parabolic dish is correct. This is because a parabolic shape is known to have the property of focusing parallel rays of light or sound to a single point, known as the focal point. In the case of an acoustic guitar, the focal point would be the hole on the top surface.

To solve this problem using ray tracing, you would need a software package that has the capability to model and analyze sound propagation. This type of software is commonly used in architectural acoustics, where the focus is on designing spaces that have good sound quality. One such software is Odeon, which is widely used in the acoustics community.

Using a ray tracing software, you can model the acoustic guitar as a 3D object and set the parameters for the shape of the back surface. The software will then calculate the paths of sound waves as they reflect off the back surface and focus at the hole on the top surface. The optimization process would involve varying the shape of the back surface and running simulations to find the shape that produces the most focused sound at the hole.

It is worth noting that this optimization process may take some time and computational power, especially if you want to consider a wide range of back surface shapes. Therefore, it would be helpful to have a clear set of predefined parameters to guide the optimization process.

In addition to using ray tracing software, there are other methods that can be used to solve this problem. One approach is to use finite element analysis (FEA) software, which can simulate the behavior of sound waves in a more detailed and accurate manner. However, this would require more advanced knowledge and skills in FEA.

In conclusion, I believe that ray tracing software is the most suitable tool for solving this problem. It is a well-established method in acoustics and has been used in various applications, including designing musical instruments. I hope this answers your question and I wish you success in your guitar design endeavors.