We can simulate physical systems on a computer:
A brief overview of physical modelling from Perry Cook. His PhD project was on voice synthesis.
A more detailed account with examples of implementations.
A range of sound examples from Julius Smith, who developed the Digital Waveguide method starting in the 80s.
A good article about the concept of physical modelling in relation to other synthesis techniques.
Developing and improving the model involves research into the acoustics of an instrument.
We can also simulate other systems such as plate reverbs. These are illustrations from Stefan Bilbao's book Numerical Sound Synthesis which explores physical models in depth and demonstrates their creative potential. The companion webpage includes quite a few examples.
You can also explore aspects of physical modelling with Sculpture in LogicPro.
Several instruments modelled (in Csound) to produce: