Physical Modeling of Musical Instruments is the rebuilding of the instruments geometry in the computer. By solving the differential equations which govern the vibration of the instruments the sound of the instrument can virtually be produced.
Therefore the sound of new geometries or the use of new material can be tested before the instrument is built in reality. All parameters can be changed here, therefore guitars, violins, pianos, percussion instrumnets, saxophones, flutes or any instrument possible can be altered to search for new sounds or a new instrument. Furthermore, completely new instruments can be invented and tested.
As high-quality sound wood for pianos, guitars or violins becomes scarce nowadays, replacing wood with new species can be tested beforehand.
In terms of metamaterials, new instrument geometries can be tried, both in terms of sound as well as stability.
The role of different parts of musical instruments in terms of the overall sound can be investigated by turning on and off certain parts of the instruments.
Finite-Difference as well as Finite-Element Time Domain methods have been used extensively to model many traditional Western instruments as well as others from all over the world.
Also electric and electronic instruments can be modeled using these methods.
One example is the Digital Guitar Workshop. Other examples can be found in the literature and respective examples on this site.
Bader, R. & Hansen, U.: Acoustical Analysis and Modeling of Musical Instruments Using Modern Signal Processing Methods. In: Handbook of Signal Processing in Acoustics. D. Havelock, M. Vorländer, S. Kuwano (ed.). Springer, 219-247, 2008.
Münster, M., Richter, J., Bader, R.: Eigenvalue shapes compared to forced oscillation patterns of guitars, Proc. Mtgs. Acoust. 19, 035001, http://dx.doi.org/10.1121/1.4799103, 2013.
Bader, R.: Whole geometry Finite-Difference modeling of the violin. In: Proceedings of the Forum Acusticum 2005, 629-634, 2005. Budapest_Violin
Bader, R.: Additional modes in a Balinese gender plate due to its trapezoid shape. In: Bader, R., Neuhaus, Ch, & Morgenstern, U. (eds.): Concepts, Experiments, and Fieldwork: Studies in Systematic Musicology. Peter Lang Verlag, Frankfurt a.M. 95-112, 2009.
Lau, B., Bader, R., Schneider, A. & Wriggers, P.: Finite-Element transient calculation of a bell struck by its clapper. In: Bader, R., Neuhaus, Ch, & Morgenstern, U. (eds.): Concepts, Experiments, and Fieldwork: Studies in Systematic Musicology. Peter Lang Verlag, Frankfurt a.M. 137-156, 2009.
Pfeifle, F. & Bader, R.: Real-Time Physical Modelling of a real Banjo geometry using FPGA hardware technology. In: Bader, R. (ed. / Hrsg.).: Musical Acoustics, Neurocognition and Psychology of Music / Musikalische Akustik, Neurokognition und Musikpsychologie. Hamburger Jahrbuch für Musikwissenschaft 25, 71-86, 2009.