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| THE DISCUSS ABOUT THE COMPLETION OF MORSE’S NORMAL-MODE FORMED SOLUTION FOR SOUND FIELD IN A ROOM |
Wan Quan, Jiang Wei-Kang
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| State key laboratory of mechanical system and vibration, Shanghai Jiao Tong University, Shanghai, 200240 |
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Abstract The classical normal-mode theory about the steady-state sound field in a room proposed by the famous physicist named Morse P M is perfect in mathematical derivation. However, some domestic researches 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 this paper, the basic assumption about the sound source in Morse’s normal-mode theory is 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 researcher’s doubts about this basic assumption. Moreover, the ray solution is 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 author thinks that Morse’s normal-mode solution for the steady-state sound field in a room is complete.
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Received: 29 April 2008
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2009, Vol. 28 
