Mechanics of musical instruments
type: Item
instance of: scholarly article
title: Mechanics of musical instruments
zbMATH Open document ID: 0861.70003
published in: CISM International Centre for Mechanical Sciences. Courses and Lectures
publication date: 1996-07-16T00:00:00Z
review text: [The articles of this volume will not be indexed individually.] The theory of musical instruments has represented since almost three centuries one of the most fascinating fields where the methods of mechanics have proved their power in order to understand and explain the working of apparatuses that for many centuries were exclusively commited to the skill of families of artisans. At the beginning of the eighteenth century, the propagation of sound through vibrating strings, air tubes, membranes, plates, shells became a problem describable by rigorous equations, able to interpret and predict the generation of sounds and their variations due to the shape of each instrument. People like Daniel Bernoulli, d'Alembert, Euler, Chladni, gave fundamental contributions to a rational theory of sound, under the unifying concept of linear wave propagation in an elastic continuum. A collection of these results and a new variational formulation of the problem of wave propagation was proposed by Rayleigh in his famous treatise ``The theory of sound'' (1894). But the response of musical instruments is not perfectly conformal to the linear model. On one hand, nonlinearity is an essential aspect of many instruments, in the sense that their dynamical responses (playability) are heavily modified by the elastic deformations. On the other hand, dissipation mechanisms are necessary for understanding decay transients or radiation. The purpose of this volume is to offer the beginner a gradual introduction to musical acoustics. The matter is ordered in seven chapters, each written by a specialist, ranging from pure mathematical theory of the simple oscillator to problems which are specific to musical instruments. The first four chapters are a compendium of classic notions about mechanical vibrations of systems with a finite number of degrees of freedom, of strings, beams, and plates. Unfortunately, there are some overlapping and some omissions. Among them the chapter one, written by \textit{P…
Mathematics Subject Classification ID: 70-02
Mathematics Subject Classification ID: 70-06
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 74F10
Mathematics Subject Classification ID: 00B15
Mathematics Subject Classification ID: 70Jxx
Mathematics Subject Classification ID: 70Kxx
zbMATH DE Number: 904958
zbMATH Keywords: Mechanics
zbMATH Keywords: Musical instruments
zbMATH Keywords: mechanical vibrations of systems with finite number of degrees of freedom
zbMATH Keywords: strings
zbMATH Keywords: beams
zbMATH Keywords: plates
zbMATH Keywords: bowed string instruments
zbMATH Keywords: violin
zbMATH Keywords: reed instruments
zbMATH Keywords: cylindrical clarinet
zbMATH Keywords: aeroacoustic phenomena
reviewed by: Piero Villaggio
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 904958