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Die Klarinette als Verzweigungssystem: Eine Anwendung der Methode der iterierten Abbildungen

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Considering the clarinet as an interactive system between linear wave propagation in the tube and nonlinear sound generation in the mouthpiece, it is possible to write the model equations in the form of a convolution integral. For very small reflection functions this representation can be reduced to the simpler one of an iterated map. A number of different nonlinear characteristics and their influence on the Feigenbaum diagram, the Lyapunov spectrum and the Feigenbaum constants are investigated.

Zusammenfassung

Betrachtet man die Klarinette als wechselwirkendes System zwischen linearer Wellenausbreitung im Rohr und nichtlinearer Schallerzeugung im Mundstück, so kann man die Modellgleichung in Form eines Faltungsintegrals schreiben. Für sehr schmale Reflexionsfunktionen reduziert sich diese Darstellung auf die einfachere einer iterierten Abbildung. Untersucht werden verschiedene typische nichtlineare Kennlinien und deren Einfluß auf Feigenbaum-Diagramm, Lyapunov-Spektrum und Feigenbaum-Konstanten.

Sommaire

On peut considérer la clarinette comme un système au sein duquel interagissent des ondes acoustiques se propageant linéairement le long du fût de l'instrument et des ondes crées non-linéairement au niveau de l' anche.L' équation régissant un tel système se formule alors au moyen d'intégrales de convolution. Dans le cas de fonctions de réflexion suffisamment étroites, cette représentation se ramène à une simple itération d'endomorphismes. On a étudié pour ce cas différentes caractéristiques nonlinéaires typiques du système, ainsi que leurs effets sur son diagramme de Feigenbaum, son spectre de Lyapunov et ses constantes de Feigenbaum.
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Document Type: Research Article

Publication date: September 1, 1990

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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