By Antoine Chaigne
This e-book, the 1st English-language translation of Acoustique des tools de musique, moment Edition, offers the required foundations for knowing the complicated actual phenomena all in favour of musical tools. what's the functionality of the labium in a flute? Which beneficial properties of an software 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 bought within the box over the last fifteen years. Their aim is to teach that ordinary actual versions can be utilized with gain for varied functions 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 song fans who desire to know about the fundamentals of musical acoustics.
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Additional resources for Acoustics of Musical Instruments
10). In general, both polarizations are excited. 2. In the absence of coupling terms in the model, and Á are independent of each other. In stringed musical instruments, however, this coupling does exist: it is mainly due to motion of the bridge at the end and to the existence of nonlinear terms for large amplitude motion (see Chap. 8). 3. Strings (and membranes) are also subjected to longitudinal vibrations. Such vibrations arise because ﬂuctuations in length induce stress ﬂuctuations. As a consequence, the stress becomes a function of the amplitude (and thus a function of time).
Strings (and membranes) are also subjected to longitudinal vibrations. Such vibrations arise because ﬂuctuations in length induce stress ﬂuctuations. As a consequence, the stress becomes a function of the amplitude (and thus a function of time). This transverse–longitudinal coupling is usually neglected under the assumption of small amplitude. Nevertheless, it can be easily observed in piano strings, for example. This point will be clariﬁed in Chap. 8. 2 Homogeneous Membranes and Strings Under Uniform Tension For a uniformly stretched membrane made of a homogeneous material, the tension tensor becomes isotropic, which can be written as D 1l, where 1l denotes the unit tensor.
Chaigne and J. 47) The hypothesis of isotropic material yields the stress tensor. Here, we write [see Eq. 26)] xx D E"xx , since the Poisson’s effect is neglected. Let us now express the elastic potential energy, also called strain energy, of the bending bar. For an elementary spring of stiffness k, the elastic energy stored under the effect of a traction (or compression) of elongation x from equilibrium is Ep D 12 kx2 . 22): dFx D xx dS. Therefore, the elementary elastic potential energy is: dEp D 12 xx "xx dx dS.
Acoustics of Musical Instruments by Antoine Chaigne