| 声场中的对称性与守恒定律 |
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| 引用本文： | 姜哲.声场中的对称性与守恒定律[J].江苏大学学报(自然科学版),2003,24(1):10-14. |
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| 作者姓名： | 姜哲 |
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| 作者单位： | 江苏大学振动噪声研究所,江苏,镇江,212013 |
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| 基金项目： | 国家自然科学基金资助项目 (5 0 0 75 0 3 6) |
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| 摘 要： | 从能量的角度讨论了稳态场中的对称性和守恒定律，采用势能密度和声压的相位函数作为基本变量，描述声场的物理性质，从两个方面给出关于基本变量的控制方程：其一，基于力学的基本定律；其二，将稳态声场看成Lagrange系统，应用变分方法得到Euler-Lagrange方程，针对Lagrange系统，应用Noether理论讨论了在对称变换群变换下的不变性，获得两个守恒量即声强和能量张量，以及对应的守恒定律。
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| 关 键 词： | 守恒定律 声场 Lagrange系统 对称性 能量守恒 |
| 文章编号： | 1671-7775(2003)01-0010-05 |
| 修稿时间： | 2002年10月20 |
Symmetry and Conservation Laws in Acoustic Fields |
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| JIANG Zhe.Symmetry and Conservation Laws in Acoustic Fields[J].Journal of Jiangsu University:Natural Science Edition,2003,24(1):10-14. |
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| Authors: | JIANG Zhe |
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| Abstract: | From the energy point of view, the symmetry and conservation laws in acoustic fields are discussed. A potential energy density and a phase function are taken as basic variables of the acoustic field. The equations about the basic variables are derived by two different approaches. One is from the basic mechanics laws. Another is taking the steady acoustic field as a Lagrangian system and using variational method to yield Euler Lagrange equations. For the Lagrangian system, by applying the Noether's theory, two kinds of energy conservations, viz the acoustic intensity and the energy tensor, are obtained. |
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| Keywords: | acoustic field Lagrangian system symmetry energy conservation |
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