The optimal shape of the reflex tube of a bass loudspeaker [Elektronische Ressource] / Jevgenijs Jegorovs

The Optimal Shape of the Re exTube of a Bass LoudspeakerJevgenijs JegorovsVom Fachbereich Mathematikder Universit at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte DissertationApril 2007The Optimal Shape of the Re exTube of a Bass LoudspeakerJevgenijs JegorovsVom Fachbereich Mathematikder Universit at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Axel Klar2.hter: Prof. Dr. Wim DesmetTag der Disputation: 25.04.2007D 386AbstractIn this thesis the author presents a mathematical model which describes thebehaviour of the acoustical pressure (sound), produced by a bass loudspeaker.The underlying physical propagation of sound is described by the non{linearisentropic Euler system in a Lagrangian description. This system is expandedvia asymptotical analysis up to third order in the displacement of the membraneof the loudspeaker. The di eren tial equations which describe the behaviour ofthe key note and the rst order harmonic are compared to classical results. Theboundary conditions, which are derived up to third order, are based on theprinciple that the small control volume sticks to the boundary and is allowed tomove only along it.