I am trying to solve a challenging problem, and I'm hoping for some advice on how to proceed. I want to model sound waves in a cavity for the purpose of determining resonance. The plan is to answer the question numerically, but I need some better bearings regarding the physics involved.
Here is a summary of my main questions:
- How should I model this situation for a closed cavity?
- What does resonance in a closed cavity even look like? (as opposed to a "whistling" kind of cavity)
- What wave equation should I use? I'm assuming spherical for an arbitrary cavity.
- I don't even know if using diff eq's (wave equation) is the best approach here. Would it be possible, or even advisable, to try modeling noise in the cavity and see what kind of response I get?
- I don't want my solution to be dependent on the location of the source inside the cavity. Rather, I want to understand what the natural frequency of the space is. Is that even possible, or am I living in a fantasy here?
I want to start by solving this problem for the cube, so that I understand all the parameters involved, and solve for general cavities from there. My naive guess at the solution for cubes (or rectangular prisms) is to look at standing waves in the 3 dimensions (though I don't know which harmonic would be dominant). The problem with this approach is that it does not translate to arbitrary cavities very well.