> Like howling of wind, the sound from musical instruments
The typical technique used to model these is a "digital waveguide" - treating the wind instrument or string as a one-dimensional tube. The wave propagating down the tube is sampled at your sample rate spatially, so the computer model consists of a pair of queues of samples propagating in each direction. A typical guitar string might have a pair of buffers 300-600 audio samples long, and you move pointers into those buffers every cycle to model the propagation. I'll link to PASP as others are doing for a diagram:
At the end of the waveguide (typically where the string is attached to the bridge, or the sound hole of a tube is), the traveling wave encounters an impedance discontinuity, exactly like an electrical wave on a transmission line would, except the units are different. This discontinuity causes the energy in the wave to reflect, and as this repeats, the string vibrates.
That's the core technique. There is so much research on top of this, backed by hard math, to model other nonlinear behaviors of strings, to add other components to the model, etc. I find it fascinating how physical modeling is very well studied within a very small circle of researchers, and nearly nobody else has heard of the concepts.
Happy to discuss further, either here or over email, if you or anyone else has questions!
The typical technique used to model these is a "digital waveguide" - treating the wind instrument or string as a one-dimensional tube. The wave propagating down the tube is sampled at your sample rate spatially, so the computer model consists of a pair of queues of samples propagating in each direction. A typical guitar string might have a pair of buffers 300-600 audio samples long, and you move pointers into those buffers every cycle to model the propagation. I'll link to PASP as others are doing for a diagram:
https://ccrma.stanford.edu/~jos/pasp/Ideal_Acoustic_Tube.htm...
At the end of the waveguide (typically where the string is attached to the bridge, or the sound hole of a tube is), the traveling wave encounters an impedance discontinuity, exactly like an electrical wave on a transmission line would, except the units are different. This discontinuity causes the energy in the wave to reflect, and as this repeats, the string vibrates.
That's the core technique. There is so much research on top of this, backed by hard math, to model other nonlinear behaviors of strings, to add other components to the model, etc. I find it fascinating how physical modeling is very well studied within a very small circle of researchers, and nearly nobody else has heard of the concepts.
Happy to discuss further, either here or over email, if you or anyone else has questions!