Chapter 3 Sound modeling: source-based approaches Federico Avanzini Copyright c 2005-2009 Federico Avanzini except for paragraphs labeled as adapted from <reference> This book is licensed under the CreativeCommons Attribution-NonCommercial-ShareAlike 3.0 license. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/, or send a letter to Creative Commons, 171 2nd Street, Suite 300, San Francisco, California, 94105, USA. 3.1 Introduction It was 1971 when Hiller and Ruiz envisioned the possibility of using numerical simulations of the wave equation for sound synthesis applications. [. . . ] This is a completely new approach to electronic sound synthesis insofar as the starting point is the physical description of the vibrating object [. . . ] A decade later McIntyre, Schumacher, and Woodhouse published their classic study on the use of non-linear maps for modeling the generation of self-sustained oscillations in musical instruments. [. . . ] a fast minicomputer could produce results at a cycle rate in the audible range. The result would perhaps have some novelty: an electronic musical instrument based on a mathematical model of an acoustic instrument [. . . ] Today the algorithms described by these authors can be easily implemented in real-time on general- purpose hardware, and it is common practice to use the term physical modeling to refer to sound modeling techniques in which the synthesis algorithms are designed based on a description of the physical phenomena involved in sound generation. Direct sound representations, that are merely based on a description of the sound waveform, do not contain information about the way the sound has been generated and processed by the surrounding environment before arriving to the listener’s ear. Sampling in time the sound signal does not assume