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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Acoustic theory ： ウィキペディア英語版 Acoustic theory Acoustic theory is a mathematical field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach. Propagation of sound waves in a fluid (such as water) can be modeled by an equation of continuity (conservation of mass) and an equation of motion (conservation of momentum) . With some simplifications, in particular constant density, they can be given as follows: : $$ \begin \frac + \kappa~\nabla \cdot \mathbf & = 0 \qquad \text \\ \rho_0 \frac + \nabla p & = 0 \qquad \text \end where $p(\backslash mathbf,\; t)$ is the acoustic pressure and $\backslash mathbf(\backslash mathbf,\; t)$ is the flow velocity vector, $\backslash mathbf$ is the vector of spatial coordinates $x,\; y,\; z$, $t$ is the time, $\backslash rho\_0$ is the static mass density of the medium and $\backslash kappa$ is the bulk modulus of the medium. The bulk modulus can be expressed in terms of the density and the speed of sound in the medium ($c\_0$) as : $\backslash kappa\; =\; \backslash rho\_0\; c\_0^2\; ~.$ If the flow velocity field is irrotational, $\backslash nabla\; \backslash times\; \backslash mathbf=\backslash mathbf$, then the acoustic wave equation is a combination of these two sets of balance equations and can be expressed as 〔Douglas D. Reynolds. (1981). ''Engineering Principles in Acoustics'', Allyn and Bacon Inc., Boston.〕 :$$ \cfrac - c_0^2~\nabla^2\mathbf = 0 \qquad \text \qquad \cfrac - c_0^2~\nabla^2 p = 0, where we have used the vector Laplacian, $\backslash nabla^2\; \backslash mathbf\; =\; \backslash nabla(\backslash nabla\; \backslash cdot\; \backslash mathbf)\; -\; \backslash nabla\; \backslash times\; (\backslash nabla\; \backslash times\; \backslash mathbf)$ . The acoustic wave equation (and the mass and momentum balance equations) are often expressed in terms of a scalar potential $\backslash varphi$ where $\backslash mathbf\; =\; \backslash nabla\backslash varphi$. In that case the acoustic wave equation is written as :$$ \cfrac - c_0^2~\nabla^2 \varphi = 0 and the momentum balance and mass balance are expressed as :$$ p + \rho_0~\cfrac = 0 ~;~~ \rho + \cfrac~\cfrac = 0 ~. ==Derivation of the governing equations== The derivations of the above equations for waves in an acoustic medium are given below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Acoustic theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.