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Revision of the Kirchhoff-Rayleigh-Theory of Sound Propagation in visco-thermal Air. Part II: Evaluation of Sound Fields in Flat Capillaries Revision der Kirchhoff-Rayleigh-Theorie zur Schallausbreitung in thermo-viskoser Luft. Teil II: Feldberechnungen in Flach-Kapillaren

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Part I of this paper has simplified the classical theory of sound in viscous and heat conducting fluids by Kirchhoff and Rayleigh in reducing their three-wave-theory to a two-wave-theory. This was achieved by an iteratitive consideration of the heat conduction. Thereby the characteristic equation for the modal eigen values was simplified. Two types of mode solutions could be discerned: the shear wave modes which exist in capillaries with a dominating shear wave, and the sound wave modes which correspond to the sound modes in ducts without losses. Whenever the counterparts in loss-free ducts are cut-off , the sound wave modes in capillaries with losses are carcino modes. By the study of the higher modes in capillaries, part I has layed the fundamentals of a modal analysis of sound fields in ducts with a lossy medium, which shall be displayed in the present part II for some typical configurations of sound field excitations and duct inhomogeneities. With such objects the formulation of adequate boundary conditions in a medium with losses shall be developed. Objects with Cartesian co-ordinates will be used for ease of the numerics. The present part II of the paper will continue the enumerations of chapters, figures, and equations from part I.

In Teil I wurde die klassische Theorie des Schalls in (gasförmigen) Medien mit viskoser Reibung und Wärmeleitung von Kirchhoff und Rayleigh vereinfacht, indem die thermischen Verluste durch eine Iteration berücksichtigt wurden. Dadurch entfällt in der klassischen drei-Wellen-Theorie eine der Komponenten-Wellen, nämlich die Temperaturwelle. Die charakteristische Gleichung für die modalen Wellenzahlen vereinfacht sich. Es konnten zwei Gruppen von Moden-Lösungen unterschieden werden, die Scherwellen-Moden in engen Kapillaren, in denen die Zähigkeitswelle dominiert, und die Schallwellen-Moden , welche den Moden bei verlustfreiem Medium entsprechen. Letztere Moden nehmen die Eigenschaften von Carcino-Moden an, wenn ihre Abbilder im verlustfreien Kanal gesperrt sind. Der Teil I legt mit seinen Untersuchungen die Basis für die Modal-Analyse von Schallfeldern in Kanälen mit thermo-viskosen Verlusten des Ausbreitungs-Mediums. Diese Darstellung von Schallfeldern mittels Moden soll in dem hier vorliegenden Teil II der Publikation für fundamentale Konfigurationen der Schallquelle und/oder der Berandung vorgeführt werden, um daran die Formulierung geeigneter Randbedingungen zu entwickeln. Dabei werden zur Vereinfachung der Numerik Objekte in kartesischen Koordinaten benutzt. Es werden in diesem Teil II die Numerierungen der Kapitel, Abbildungen und Gleichungen von Teil I fortgesetzt.
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Document Type: Research Article

Publication date: September 1, 2007

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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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