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Changing the Shape of Lossless n-Tubes

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In this paper we investigate analytically the acoustical effects of small changes of the shape of lossless n-tubes. We derive, by means of a decomposition method, general formant shift formulae for n-tubes. This method is not based on the use of eigenfunctions, but on the geometrical interpretation of the n-tube formula in the formant space. We give some examples of classes of changes of tube shape with their acoustical effects in the F 1, F 2-plane.


In dieser Arbeit werden die akustischen Effekte von kleinen Formänderungen bei verlustfreien n-Rohren analytisch untersucht. Wir leiten mit Hilfe eines Zerlegungsverfahrens allgemeine Formeln für die Verschiebung der Formantfrequenzen von n-Rohren ab. Diese Methode gründet sich nicht auf den Gebrauch von Eigenfunktionen, sondern auf die geometrische Interpretation der n-Rohr-Formel im Formantraum. Wir zeigen einige Beispiele von Formänderungsklassen und ihren akustischen Effekt in der F 1-F 2-Ebene.


On étudie par une voie analytique les effets acoustiques causés par de petits changements de la forme des n-tubes sans pertes. A l'aide d'une méthode de décomposition, on établit des formules générales donnant le déplacement de fréquence des formants en fonction de ces variations de forme. Cette méthode ne se sert pas des fonctions propres, elle utilise une interprétation géométrique de la formulation donnée antérieurement et liant les n-tubes à l'espace des formants. Nous donnons pour finir quelques exemples de changements de forme avec leurs effets acoustiques dans le plan (F 1, F 2).
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Document Type: Research Article

Publication date: August 1, 1983

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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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