外文翻譯--平面波(文件)
【正文】 ve the variable. It will be clear from the context of the discussion if the quantity is in the frequency or in the time domain. The Fourier transform of Euler’s equation, Eq .(), bees, in the frequency domain 0i vp?? ?? () where Eq.() has been used again for the time derivative. Time Averaged Acoustic Intensity Now consider the intensity relationship for steady state fields .This is defined as the average of the instantaneous intensity over a period T, where T=1/f and f is the excitation frequency: 0() 1 ( ) ( )TI p t v t d tT? ? ? () Using plex variable notation this relationship bees 12() Re ( ( ) ( ) )I pv? ??? ? () where stands for plex plex conjugate and Re for the real part .The onehalf results from the time average process .I is the average power over one period passing through unit area. For example , the x ponent of this flow xI represents the power passing through an element of area yz?? . Important in this chapter is the radiation from planar radiators .Of particular interest is the power flow crossing an infinite plane. For example, consider the total power crossing the corrdinate plane z=0, a quantity expressed is watts or joules persecond .We use the symbol ()?? to represent the total power in watts crossing the boundary: () ( , , 0 )zI x y d x d y? ???? ???? ?? () If there are no sources in the upper half space, then ? is the total power radiated by 0zz? has the same power passing through it, since is no absorption in the fluid and there are no sources above the boundary. The equation of continuity,Eq.(), bees 01 ( ) ( 0 ) ()T e e T ed t IT t T ???? ? ? ? ??? () By the definition of stesdy state the energy density at time at time T is the same as the density at time 0, so that we have ( ) 0I ??? ? () This means that in a sourcefree field the divergence of the time averaged acoustic intensity must always be zero. The only way the intensity field can have a nonzero divergence is if there are sources or sinks of energy within the medium, or losses in the medium. Plane Wave Expansion We turn now to plane wave solutions of the wave equation in Cartesian coordinates .These solutions will be useful in the study of sources which are planar (or nearly planar) in geometry such as vibrating plates .We note that Eq.() is very similar to the equation for a vibrating string。下面我們從一些基本概念引出平面波方程， Euler’s方程，和聲學(xué)的強度的概念。 三個置換協(xié)調(diào)方向用 u， v，和 w表示。 總壓力是一等級的數(shù)量。 我們首先命令 p(x+? x,y,z)一個 Taylor系列作為被引入量 .力的箭頭方向表示力的正方向 .，力在 x的正方向延伸 . ( , , ) ( , , ) pp x y z p x x y z y z x y z x?? ? ? ? ? ? ? ? ? ? ? 我們現(xiàn)在調(diào)用 Newton’s方程 , f =ma =m ut??， 在其中 f是力 ， 0? 是流體密度 ， 得出 0 uptx? ???? 在 y和 z方向?qū)嵭型瑯拥姆治龅贸鋈缦聝蓚€方程：
畢業(yè)設(shè)計相關(guān)推薦
鄂ICP備17016276號-1