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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**Sample text**

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).