By Paul Filippi,Aime Bergassoli,Dominique Habault, et al.Elsevier|Elsevier Science||Academic PressAdult NonfictionScience, TechnologyLanguage(s): EnglishOn sale date: 31.05.2011Street date: 23.09.1998
The e-book is dedicated to the very foundation of acoustics and vibro-acoustics. The physics of the phenomena, the analytical tools and the fashionable numerical concepts are offered in a concise shape. Many examples illustrate the basic difficulties and predictions (analytic or numerical) and are frequently in comparison to experiments. a few emphasis is wear the mathematical instruments required via rigorous idea and trustworthy prediction methods.
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Additional info for Acoustics. Basic Physics, Theory, and Methods
E. the normal to the wavefront. e. 61) This is the same result as for a plane wave, replacing the unit direction vector of the plane wave by the unit radial vector of the spherical wave. e. the acoustic impedance of the wave, equals, as for plane waves, the characteristic impedance of the medium Z0 = ρ0c0. At large distance a spherical wave behaves locally like a plane wave. For a spherical diverging harmonic wave of angular frequency ω with time dependence e‒ιwt (classical choice in theoretical acoustics), one has f+(ξ) = A+e‒ιwξ and so Φ=A+|x→|e−ιω(t−(|x→|/c0))=A+|x→|e−ιωte+ιk|x→|,withk=ωc0thewavenumber Thus, p1=−ρ0∂Φ∂t=ιωρ0A+|x→|e−ιωte+ιk|x→|=ιωρ0Φ,υ→1=∇Φ=ιk[1−1ιk|x→|]A+|x→|e−ιωte+ιk|x→|n→=ιk[1−1ιk|x→|]Φn→ and the relation between acoustic pressure and acoustic velocity becomes: υ→1=[1−1ιk|x→|]p1ρ0c0n→ and the large distance condition becomes k|x→|≫1, or, introducing the wavelength λ = 2π/k, |x→|≫λ/2π.
Then equations of acoustics are simply obtained by linearization of the equations of the mechanics of continua. The main phenomenon encountered in acoustics is wave propagation. This phenomenon is the only one that occurs in an infinite homogeneous medium. A second important phenomenon is scattering, due to the various obstacles and inhomogeneities encountered by the wave. A third, more tenuous, phenomenon is absorption and dispersion of waves, due to dissipation processes. The first and second phenomena need only a simple methodology: derivation of a wave equation and of a boundary condition from the linearized equations of the mechanics of continua for a homogeneous, steady, perfect simple fluid or elastic solid.
Thesis. The reason for writing this book was, at the time we began, the lack of textbooks. Most of the books were either too specialized, and thus almost incomprehensible for students, or too exhaustive. We needed a basic course which could be presented within a rather short period of time to students who had a fair background in Mathematics and Mechanics but often no knowledge of Acoustics. The purpose of this book is to present the main basis of modelling in Acoustics. The expression ‘modelling’ used here includes the procedures used to describe a physical phenomenon by a system of equations and then to solve this system by analytical and/or numerical methods.
Acoustics. Basic Physics, Theory, and Methods by Paul Filippi,Aime Bergassoli,Dominique Habault, et al.Elsevier|Elsevier Science||Academic PressAdult NonfictionScience, TechnologyLanguage(s): EnglishOn sale date: 31.05.2011Street date: 23.09.1998