# Acoustics of Musical Instruments by Antoine Chaigne

By Antoine Chaigne

This e-book, the 1st English-language translation of ** Acoustique des tools de musique, moment Edition**, provides the mandatory foundations for realizing the advanced actual phenomena fascinated by musical tools. what's the functionality of the labium in a flute? Which positive aspects of an device let us make a transparent audible contrast among a clarinet and a trumpet? With the aid of quite a few examples, those questions are addressed intimately. The authors concentration particularly at the major effects got within the box over the last fifteen years. Their target is to teach that uncomplicated actual types can be utilized with profit for numerous purposes in sound synthesis, tool making, and sound recording. The ebook is basically addressed to graduate scholars and researchers; but it may be of curiosity for engineers, musicians, craftsmen, and tune fans who desire to find out about the fundamentals of musical acoustics.

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4). i D f1; 2; 3g/. 23) In total, on each side of the elementary volume, we get nine components ij which reduce to six components, due to symmetry. This set, denoted , is the stress tensor for the continuous medium. It is a symmetric tensor of rank 2, as for the strain tensor. 24) T D :n is the stress vector on the surface. Finally, in the presence of a body force ﬁeld f , and taking further the inertial forces into account, the local equilibrium equation in a given solid element of density is written: R D div C f ; where R is the local acceleration.

27) where Aijkl represents the elasticity tensor of the material, also denoted A. It is a fourth rank tensor. In theory, this tensor should have 34 D 81 distinct components. However, if we recall that and " are symmetrical, it reduces to 36, which is the maximum number of independent components for A. Because of additional energetic considerations, this number is reduced to 21 in the case of an anisotropic material [8]. Finally, taking also the symmetry of the material into account allows to reduce again the number of elasticity components.

26) σxx σe S L E 0 F εxx 1 Continuous Models 13 where E (in N/m2 ) is the Young’s modulus of the material. One important point here is that the stress is proportional to the strain: we are in the situation of a linear elastic behavior. This relationship, based on experimental facts, is also called Hooke’s law. 26) does not take the variation of the cross-section in the body consecutive to elongation (or compression) into account. This can only be done with the 3D generalization of Hooke’s law (see the next section).