The Study On Point Sound Reflection In Spherical Conformation

From Ten thousand temples of Rome,the Florence Cathedra in the Renaissance,Conference hall of the United Nations'headquarters,to the Chongqing people's hall, architect use spherical conformation to create colorful form and inner space, but the sound focus caused by spherical conformation become the difficult problem in architectural acoustic design, especially the reflection in hard surface, could become the imaging sound source. In the hall with short vibration time, could even hear"the second sound source". How to control the sound condition of the hall with spherical conformation is a problem which can not be ignored in inner acoustic design.The study result we get already was the quantitatively calculation method of sound reflection rules in hemisphere by surface sound, but in real problem, more problems are caused by point sound. making a report,singing song and performing by one person,one loudspeaker are all point sound. More performers and more loudspeakers are combination by point sounds, in a certain quantity, can be regard as surface sound. With the sound source of point sound, the sound condition in spherical conformation can be different greatly with the relative place changing by point sound, so it is more difficult than surface sound.At the basis of acoustic theories we get already, establish the mathematics model of hemisphere space. Expanding the sound line reflection from in semicircle to in hemisphere, simulating point sound at any position in hemisphere with coordinates rotating. The sound reflection problem in space could be solved by sound reflection analyzing and mathematical calculation in plane. Work out the first envelope curve and the second envelope curve of the sound reflected line with the point sound at any position in hemisphere, work out the formula of first envelope surface and the second envelope surface. Prove the reliability of the function with mathematics software of Mathematica5.0 and experimentation, purpose the principle and method of acoustic design in spherical conformation.There are five chapters in this paper:Chapter 1 Recapitulative expatiate the value, signification, intention, method, tool.Chapter 2 Discuss the related concepts of sound line reflected in semicircle, establish the mathematics model of hemisphere space. The sound reflection rules in hemisphere should divided to three conditions, study the rules of sound line reflected in semicircle, get the condition of sound line reflection and distribution in hemisphere with coordinates rotating , work out the first envelope curve and the second envelope curve of the sound reflected line in hemisphere. The get the envelope surface in the space of hemisphere. Verify the first envelope curve and the second envelope curve from different angle ,such as :with drawing reflected sound line,to trace the point by calculating the formula,mathematics software of Mathematica5.0.Chapter 3 Use the way of testing model to prove the reliability of the rules. Evaluates the rules, and analyze the experiment.Chapter 4 Compare the difference and relationship of sound field in hemisphere by point sound and surface soundChapter 5 The conclusion and to prospect the research for the future.