I've been thinking about posting this question on Music Performance stack, but finally I think it fits more here since I'm interrested in technical details.
The subject of resonance of a tube of air is pretty well documented for simple shapes, like cylinders (open of closed), cones, closed rectangular boxes, spheres et cetera. I even found formulas in my high school books.
But I am interested in much more complex case. Let's imagine we have a solid tube with a certain shape with holes in it filled with vibrating air of frequency $f_i$. How can we predict the frequency $f_o$ of air that come outside of the tube?
For now I can imagine only two ways.
- Decompose the problem into sub-problems, in this case complex shape into much simpler shapes (cylinders, cones, rectangular boxes, spheres etc). But still I have no idea how a whole in the tube would affect the frequency, I suppose we would need to take in count the placement of this whole and its size.
- Run a computer simulation of such system. This would require knowledge how does the frequency propagade through air in such solid tube.
To simplify a little bit this complex problem let's forget conditions like air temperature, pressure and humidity. I'm more interrested in second approach, to create a tool that works a little bit like fuild mechanics simulation software, that help for example design heating installations etc cetera, except that this tool would be usefull for acoustic installations, architecture or instrument design.
If anyone could share some knowledge usefull to understand this phenomena I would be greatfull. What I have found in school and university books or wikipedia is not enough, or I'm not searching for right words.