If you are using waveguides for a physical model, you shouldn’t need to do anything so complicated as actively search for common harmonics because like a string, a waveguide will resonate naturally at any frequency that is a harmonic of the fundamental. The great thing about waveguides is that they can produce a recognizable string-like sound just by exciting them with an impulse like a click or short noise burst. If you then take the output of the “struck” waveguide and use that to excite all the open strings with an attenuated version of the signal produced by the struck string, you will also produce sympathetic resonances like you would get in a piano.
At the basic level, it’s not super complex. You can basically feed an impulse into a tuned delay line, then feed the output of that (at an appropriately reduced amplitude) into another tuned delay line, and you’ll be on your way to a rudimentary physical model with sympathetic resonance. The complexities of physical modeling mostly have to do with modeling deviations from an ideal string, the dampening of the various materials that comprise the instrument, and the feedback between the various strings. The specifics of that are mostly beyond my knowledge, though.
Read more here: Source link