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Download e-book for kindle: Acoustics: basic physics, theory and methods by Paul Filippi, Aime Bergassoli, Dominique Habault, Jean

By Paul Filippi, Aime Bergassoli, Dominique Habault, Jean Pierre Lefebvre

The publication is dedicated to the very foundation of acoustics and vibro-acoustics. The physics of the phenomena, the analytical tools and the fashionable numerical recommendations 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 conception and trustworthy prediction methods.

  • A series of sensible difficulties, which mirror the content material of every chapter
  • Reference to the most important treatises and primary contemporary papers
  • Current computing concepts, utilized in challenge solving

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29 P H Y S I C A L B A S I S OF A C O U S T I C S plane (O, y, z) with Ox colinear with the normal ff to the surface in the direction (1) ~ (2) ( f f - (1, 0, 0)). Consider a plane harmonic wave impinging from (1) on the surface with velocity potential ff~i of amplitude ~I'0, unit propagation vector n-'/= (cos 01, sin 01, 0) (such that (if, if1)-Oi), angular frequency w (with time dependence e - U " t ) , wavenumber k (1) - - ~ 3 / c (1)" t~l ~ '~oe-U~ +~k~ ~ -- t~oe-tWte +~k~ c o s 01 + y sin 01) The two media being half-infinite, this wave gives rise to two plane waves" 9 In medium (1) a reflected wave ~g with direction vector fig - (cos 0g, sin OR, O) (such that (if, f i g ) - 0g) and amplitude r~" t~)R _.

A surface such that the acoustic field at a given point of the surface depends only on the properties of the surface at this point. r -= ( V r h'r~)r~ Then O~p 1 ~op~ - ~kp~ - ~-k with ~ = Zn/Zo the reduced (dimensionless) normal impedance of the surface or the specific normal impedance of the surface. " BASIC PHYSICS, T H E O R Y AND METHODS specific normal impedance ft. e. with direction f i r - ( - c o s 0i, sin Oi, 0). Then one has, using the same notation as for the penetrable interface, - ~oe-tWte +&Y sin O,[e+~kx cos O, + re-'kx cos o,] with r the reflection coefficient for pressure or potential.

Assume that the boundary cr is made of a perfectly rigid solid which forces the normal particle velocity ft. V(M, t) to be zero. 2) C H A P T E R 2. 43 ACOUSTICS OF ENCLOSURES where the normal derivative On~(M, t) is defined by the scalar product On~(M, t) = if(M). V~(M, t) The corresponding boundary value problem is called the Neumann problem. The Dirichlet boundary condition. Assume that the fluid which the acoustic wave is propagating in is a liquid which is in contact with a gas along a (an example is the surface of the sea).

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