Studies Of The Steady-state Solution Of Room Acoustic With Absorption

The research of model rectangular room is a main question about the sound field in theroom. The analysis and research acoustic source that produces the sound field in the room, is themost basic acoustics question in the room. Morse has produced the three dimensionalprogression solution form of rectangular room, but it is limited by computation speed, theduplicate root of Eigen function has not solved. Although Morse proposed the picture law, thismethod has the very big limitation, only can figure out several roots, does not have anysignificance, calculated the huge root also is impractical.The identical wall surface has the same acoustic impedance rate about the rectangular room,the corresponding Eigen function may obtain, it may express three unidimensional Eigenfunction product, the three-dimensional problem transfers three unidimensional questions tosolve in other words. The boundary of the absorbed energy also face how to solve the massiveroots of the duplicate transcendental equation, therefore the paper proposed a method about howto ask the duplicate characteristic value of the duplicate transcendental equation. Through thedetermination of starting value, uses the Newton iteration method, may further extract theapproximate value, the leak root about the duplicate characteristic value also may carry on thefurther discussion. The Eigen function method is a question of completeness that has based onthe Eigen function collection. If the Eigen function collection also has completeness when thecharacteristic value is a plural number, this is a question that this article must discuss. This articlenamely makes some discussions that based on the modern computation fast characteristicthrough some examples through the exact solution and the progression solution contrast, thuscauses the progression solution to change even more concrete application, has the profoundunderstanding regarding the completeness of Eigen function collection.It inferred the steady state solution of the sound field in the room in the point source drive.The steady state solution may achieve the sum of the spatial function table a series of Eigenfunction by the Eigen function method. Then the research of the rectangular room steady statesolution that the surface of wall is rigid and the air dielectric has the small absorption, throughthe equation development, has promoted the mirror image source. Simultaneously, it confirmed in the steady state solution to conceal the direct link sound.The wall surface of the rectangular room has the absorption. Morse's solution is thesuperimposition of the three dimensional progression, it is difficult to confirm the completenessfrom mathematics, we use a physical process to confirm, through an energy method, it confirmsthe complete question about the three dimensional progression that has the duplicatecharacteristic value.Because the progression form solution restrains slowly in the near sound field, thisintensified the computation complexity, needs massive tedious computations through the Eigenfunction method, and therefore, the mirror image source can count the approximate solutionthrough the simple computation. It carries on the comparison through the mass data, which canfind applicable scope of the mirror image source about the sound field solution in the room. It isa fast and simple method.