外文翻譯--平面波-免費閱讀
【正文】 這樣， sc 在 x 方向上到達(dá)的頂峰的速度被定義波的階段速度。 例如， x的組成部分的穿過該區(qū)域的一個元素的力的功率。 它的研究重點在理解聲學(xué)中的一定的能量關(guān)系。 Eq.()的由來在對 p的物理意義的理解時是有用的。 222 2 21 0sx c t?????? () where? is normal displacement of the string, and sc is the wave speed, a constant. A solution to this equation is given by ( ) ( )( , ) xxi k x w t i k x w tx t A e B e? ? ? ??? () where A and B are arbitrary constants. For this solution to satisfy Eq.() we must have /xsk w c? () We introduce the string solution to understand the plane wave solutions of Eq.(). In Eq .() xk is called the wavenumber in the x direction. Consider the phase term in Eq. () given by ( , ) xx t k x t????. We track the crest of a wave traveling down the string by choosing a constant value of phase and then following it as a function of position and time .The position of the crest .Choosing 0?? arbitrarily, is given by / xsx t k c t???. Thus , sc is the velocity of the crest in the positive x direction and is called the phase velocity of the wave. The solution corresponding to the second term in Eq. () is a wave traveling in the negative x direction. At a fixed time the phase repeats over a distance xx ??? .Over this distance the phase term in Eq.() changes by 2? , giving 2 x x xk x k??? ? ? , leading to the important relationship 2/xxk ??? () x? is the wavelength in the x direction and is the distance over which the phase of the wave changes by 2? when time is held constant. 第二章 平面波 在這章中我們提出傅立葉平面波擴展的基礎(chǔ)。 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 。 Eq.()的右邊方程表明在其中有效的區(qū)域中沒有來源。 如果在第 ，那么一種力將朝著 p(x,y,z)? y? x方向延伸。在該地區(qū)中心有一個增加的能量密度時間 ,，該時間內(nèi)是能量是減弱的 . 在頻率領(lǐng)域 ,我們考慮通過解決轉(zhuǎn)變現(xiàn)象獲得穩(wěn)定的狀態(tài) . () 1 ()2 iw tpt p w e d w? ? ???? ? () 穩(wěn)定的狀態(tài) () () iwtpw p t e dt???? ? () 方程 ( )關(guān)于時間得出重要的關(guān)系 ( ) 1 ()2 i w tpt iw p w e d wt ? ? ???? ??? ? 因此 ( ()) ( )f pt iw p wt? ??? () Calligraphic理論中 f代
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