论莫尔斯的室内声场简正波理论解的完备性  

Discussion about the completion of Morse's normal-mode solution for sound field in a room

作　　者：万泉[1] 蒋伟康[1] 

机构地区：[1]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《振动与冲击》2009年第2期111-116,共6页Journal of Vibration and Shock

摘　　要：物理学家莫尔斯提出的室内受迫振动简正波理论在数学处理上无懈可击,但是,其声压解全部由简正波组成,无法直接观察到直达声的存在,因此,近些年来受到国内一些学者的置疑:该简正波理论解是包括直达声的全部解,还是不包括直达声的部分解?在傅里叶分析和狄拉克函数的基础上,经过严格的数学推导,证明莫尔斯简正波理论关于室内声源的基本假设是正确的,其物理涵义是:室内任意一个声源分布及由室内壁面反射引起的一系列镜像声源组合后可表示为分立简正函数的迭加,回答了国内一些学者对莫尔斯的室内声源基本假设的置疑。此外,在空间域上由简正波解推导出了射线解,证明室内受迫振动简正波理论与镜像原理完全等价。据此,认为简正波理论解是室内稳态声场的完备解。The classical normal-mode theory about the steady-state sound field in a room proposed by the famous physicist Morse P M is perfect in mathematical derivation.However,some domestic researchers cast doubt on this theory since its solution about the steady-state sound field in a room is purely composed of normal modes,and the direct sound cannot be found directly in this normal-mode solution.Is this solution the complete solution that contains both the direct sound and the reverberant sound,or just a partial solution without containing the direct sound field? In the paper,the basic assumption about the sound source in Morse's normal-mode theory was shown correct by one rigorous derivation,which indicates that one arbitrary sound source in a room with the addition of its all image sources resulted from wall reflection can be represented by discrete normal functions.This conclusion may interpret some researchers' doubts about this basic assumption.Moreover,the ray solution was derived directly from the normal-mode solution in spatial domain,which demonstrates that Morse's normal-mode theory is absolutely equivalent to the acoustical image source theory of room acoustics,in case of rectangular shaped room with rigid walls.Hereby,the present authors think that Morse's normal-mode solution for the steady-state sound field in a room is complete.

关 键 词：简正波 镜像源 射线解 狄拉克函数 

分 类 号：TN112[电子电信—物理电子学]