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Physical modelling synthesis is the synthesis of sound by using a set of equations and algorithms to simulate a physical source of sound. When an initial set of parameters is run through the physical simulation, the simulated sound is generated.
For example, to model the sound of a drum, there would be a formula for how striking the a drumhead injects energy into the formula that describes the resonance and damping of the drumhead. Another formula could then be applied to mimic the separate resonance of the cylindical body of the drum.
Similar stages to be modelled can be found in instruments such as a violin, though the energy impulse in this case is provided by the slip-grab behavior of the bow, the resonance and damping behavior of the strings, the transfer of string vibration through the bridge, and finally, the resonance of the soundboard in response to those vibrations.
Although physical modelling was not a new concept in acoustics and synthesis, it wasn't until the development of the Karplus-Strong algorithm, the subsequent refinement and generalization of the algorithm into digital waveguide synthesis by Julius O. Smith III and others, and the increase in DSP power in the late 1980s that commercial implementations became feasible.
Yamaha signed a contract with Stanford University in 1989 to jointly develop digital waveguide synthesis, and as such most patents related to the technology are owned by Stanford or Yamaha.
The first commercially available physical modelling synthesizer made using waveguide synthesis was the Yamaha VL1 in 1994.
Examples of physical modelling synthesis:
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