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 equipment and the fashionable numerical recommendations are provided in a concise shape. Many examples illustrate the elemental difficulties and predictions (analytic or numerical) and are frequently in comparison to experiments. a few emphasis is wear the mathematical instruments required by means of rigorous idea and trustworthy prediction methods.

- A series of functional difficulties, which mirror the content material of every chapter
- Reference to the main treatises and basic contemporary papers
- Current computing innovations, utilized in challenge solving

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**Extra resources for Acoustics: basic physics, theory and methods**

**Example text**

59 A C O U S T I C S OF E N C L O S U R E S p,c iOt ~Ct 0 L Fig. 2. Scheme of the one-dimensional enclosure. where /5(x, t) (resp. /5'(x, t)) stands for the acoustic pressure in the first (resp. (x, t) and V'(x, t) are the corresponding particle velocities; Y(t) is the Heaviside step function ( = 0 for t < 0, = 1 for t > 0). Because the aim of this academic problem is to point out the main phenomena which occur in room acoustics, attention will be paid to the function P(x, t) only. It is useful to associate to /5(x, t) (resp.

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 _.

E. 75) 30 A CO USTICS: B A S I C P H Y S I C S , T H E O R Y A N D M E T H O D S called the Snell-Descartes laws. 76) In practice one is interested in reflection and transmission coefficients for the acoustic pressure p l. e. p 1 (l) _ _ p 1 (2) = Po(e-,,,te +t,k(l)(x c o s Ol q- y sin 0t) _[_ rpe-,Vte Potpe-,~te +~k(2~(x cos Or+ y sin Or) +t,k(l)(x c o s OR nt- y sin 0R)) with P 0 - - bo-;P(l)(I)0 where rp and tp are defined as the reflection and transmission coefficients for the acoustic pressure (of the interface E).