外文翻譯--平面波(已修改)
2025-06-01 07:02 本頁面
【正文】 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 Rayleigh integrals ,the Ewald sphere construction of farfield radiation, the first product theorem for arrays, vibrating plate radiation, and radiation classification theory. Finally,a new tool called supersonic intensity is introduced which is useful in locating acoustic sources on vibrating begin the chapter with a review of some fundamentals。 the wave equation, Euler’s equation, and the concept of acoustic intensity. The Wave Equation and Euler’s Equation Let p(x,y,z,t) be an infinitesimal variation of acoustic pressure from its equilibrium value which satisfies the acoustic wave equation 22221 0pp ct?? ? ?? () for a homogeneous fluid with no viscosity .c is a constant and refers to the speed of sound in the medium .At 020C c=343 m/s in air and c=1481 m/s in water. The right hand side of Eq.() indicates that there are no sources in the volume in which the equation is valid. In Cartesian coordinates 2 2 222 2 2x y z? ? ?? ? ? ?? ? ? A second equation which will be used throughout this book is called Euler’s equation, 0 v pt? ? ???? () Where v (Greek letter upsilon) represents the velocity vector with ponents u ,v ,w 。 v ui vj wk? ? ? () where i j and k are the unit vectors in the the x, y, and z directions, respectively, and the gradient in terms of the unit vectors as i j kx y z? ? ?? ? ? ?? ? ? () We use the convention of a dot over a displacements quantity to indicate velocity as is done in Junger and Feit. The displacements in the three coordinate directions are given by u, v, and w . The derivation of Eq.() is useful in developing some understanding of the physical meaning of p and v . Let us proceed in this direction. Fig : Infinitesimal volume element to illustrate Euler’s equation Figure shows an infinitesimal volume element of fluid? x? y? z, with the x axis as shown .All six faces experience forces due to the pressure p in the fluid. It is important to realize that pressure is a scalar quantity. There is no direction associated with it .It has units of force per unit area , 2/Nm or following is the convention for pressure, P﹥ 0 → Compression P﹤ 0 → Rarefaction At a specific point in a fluid .a positive pressure indicates that an infinitesimal volume surrounding the point is under pression ,and forces are exerted outward from this volume. It follows that if the pressure at the left face of the cube in Fig. is positive, then a forc
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