Modelling attempts to replicate laws of physics that govern sound production, and will typically have several parameters, some of which are constants that describe the physical materials and dimensions of the instrument, while others are time-dependent functions describing the player's interaction with the instrument, such as plucking a string, or covering toneholes.
Incorporating this, a larger model would simulate the properties of the membrane (mass density, stiffness, etc.
Further, it may also contain an articulatory model to control the vocal tract shape in terms of the position of the lips, tongue and other organs.
Although physical modelling was not a new concept in acoustics and synthesis, having been implemented using finite difference approximations of the wave equation by Hiller and Ruiz in 1971[citation needed], it was not until the development of the Karplus-Strong algorithm, the subsequent refinement and generalization of the algorithm into the extremely efficient digital waveguide synthesis by Julius O. Smith III and others,[citation needed] and the increase in DSP power in the late 1980s[2] that commercial implementations became feasible.
[4][5] While the efficiency of digital waveguide synthesis made physical modelling feasible on common DSP hardware and native processors, the convincing emulation of physical instruments often requires the introduction of non-linear elements, scattering junctions, etc.