Acoustics. Basic Physics, Theory and Methods by P. Filippi, et al.

By P. Filippi, et al.

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Nature of liquid crystalline country has been of specific curiosity to representatives of other branches of typical sciences (physics, chemistry, biology) considering that its discovery in 1888. the main designated examine of liquid crystals (LC) started within the Nineteen Seventies whilst the importance of LC for expertise (electro-optical units, thermography) was once proven.

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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).

PHYSICAL 35 BASIS OF ACOUSTICS that is Op -- + v . (p~) - o Ot - - + ~7. ~-ff POt m + ~7. 88) -0 Tp Ot The result is Op 1 --~--t + p O V . 1 _ / ~ l Ot S 1 -- ct-O As for perfect fluids, small perfectly elastic movements are isentropic. 14), 1 _ A~ tr (e 1)i + 2#~ 1, and if one chooses as variable the elementary displacement gl. #0(V " (V/~I) _3t_V" (Tvu'I)) -- (A 0 d- #O)v(V 9 + ],t ~ (V/~ 1) = (AO + 2 # o ) v ( V . ~,1) _ ~0~7 X ~7 X ~,1, since V . (VzT)- V ( V . 2. e. with V • f f l _ 0 and V .

84) 33 CHAPTER 1. e. to a surface with normal impedance infinitely smaller than the characteristic impedance of the propagation medium (sea surface in underwater acoustics for example). The Neumann condition corresponds to the inverse situation: a surface with normal impedance infinitely larger than the characteristic impedance of the propagation medium (rigid wall in aeroacoustics for example). 10. Units, orders of magnitude The two main propagation media are air (aeroacoustics) and water (underwater acoustics).

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