TAILIEUCHUNG - Báo cáo hóa học: " Physical Modeling of the Piano"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Physical Modeling of the Piano | EURASIP Journal on Applied Signal Processing 2004 7 926-933 2004 Hindawi Publishing Corporation Physical Modeling of the Piano N. Giordano Department of Physics Purdue University 525 Northwestern Avenue West Lafayette IN 47907-2036 USA Email ng@ M. Jiang Department of Physics Purdue University 525 Northwestern Avenue West Lafayette IN 47907-2036 USA Department of Computer Science Montana State University Bozeman MT 59715 USA Email jiang@ Received 21 June 2003 Revised 27 October 2003 A project aimed at constructing a physical model of the piano is described. Our goal is to calculate the sound produced by the instrument entirely from Newton s laws. The structure of the model is described along with experiments that augment and test the model calculations. The state of the model and what can be learned from it are discussed. Keywords and phrases physical modeling piano. 1. INTRODUCTION This paper describes a long term project by our group aimed at physical modeling of the piano. The theme of this volume model based sound synthesis of musical instruments is quite broad so it is useful to begin by discussing precisely what we mean by the term physical modeling. The goal of our project is to use Newton s laws to describe all aspects of the piano. We aim to use F ma to calculate the motion of the hammers strings and soundboard and ultimately the sound that reaches the listener. Of course we are not the first group to take such a Newton s law approach to the modeling of a musical instrument. For the piano there have been such modeling studies of the hammer-string interaction 1 2 3 4 5 6 7 8 9 string vibrations 8 9 10 and soundboard motion 11 . Nice reviews of the physics of the piano are given in 12 13 14 15 . There has been similar modeling of portions of other instruments such as the guitar 16 and of several other complete instruments including the xylophone and the timpani 17 18 19 . Our work is inspired by and builds on this previous .

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