外文翻譯--平面波-wenkub
2023-05-19 07:02:13 本頁面
【正文】 above three equations into one using vectors yielding Eq() above, Euler’s Equation. Instantaneous Acoustic Intensity It is critical in the study of acoustics to understand certain energy relationships. Most important is the acoustic intensity vector. In the time domain it is called the instantaneous acoustic and is defined as ( ) ( ) ( )I t p t v t? , () with units of energy per unit time (power) per unit area, measured as (joules/s)/ 2m or watts/ 2m . The acoustic intensity is related to the energy density e through its divergence, e It? ????? , () where the divergence is yx zI II Ix y z? ? ? ?? ???? ? ? () The energy density is given by 2211022| ( ) | ( )e v t p t??? ? () where? is the fluid pressibility, 201c? ?? () Equation () expresses the fact that an increase in the energy density at some point in the fluid is indicated by a negative divergence of the acoustic intensity vector。外文部分 Chapter2 Plane waves Introduction In this chapter we present the foundations of Fourier acousticsplane wave material is presented in depth to provide a firm foundation for the rest of the book ,introducing concepts like wavenumber space and the extrapolation of wavefields from one surface to another .Fouries acoustics is used to derive some famous tools for the radiation from planar sources。 the intensity vectors are pointing into the region of increase in energy density. Figure should make this clear. If we reverse the arrows in Fig. , a positive divergence results and the energy density at the center must decrease, that is, et?? ﹤ 0. This case represents an apparent source of energy at the center. : Illustration of negative divergence of acoustic intensity. The region at the center has an increasing energy density with time ,that is, an apparent sink of energy. Steady State To consider phenomena in the frequency domain ,we obtain the steady the steady state solution through transforms () 1 ()2 iw tpt p w e d w? ? ???? ? () leading to the steady state solution () () iwtpw p t e dt???? ? () Equation () can be differentiated with respect to time to yield the important relationship ( ) 1 ()2 i w tpt iw p w e d wt ? ? ???? ??? ? so that ( ()) ( )f pt iw p wt? ??? () where the calligraphic letter f represents the Fourier transform of the time domain wave equation,Eq,(), yielding the Helmholtz equation 220p k p? ?? () where the acoustic wavenumber is k=w/c,the frequency is given by 2 f??? , and p is the function (x,y,z,? ).For simplicity of notation we drop the bar abo
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