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Weakly Nonlinear Gas Oscillations in Air-Filled Tubes; Solutions and Experiments

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The results of a theoretical and experimental investigation into the nonlinear, planar propagation of an acoustic signal in a cylindrical air-filled tube is presented. Assuming weakly nonlinear propagation and the distance of propagation smaller than the shock formation distance, the validity of the generalised Burgers' equation is analysed. The theoretical study is based on a dimensional analysis of the conservation equations followed by a calculation using asymptotic expansions. The deduced generalised Burgers' equations are solved whatever the boundary conditions are, with a numerical finite-difference method and using a harmonic balance method. Two cases are investigated experimentally: the purely progressive case, and the standing wave with an unknown termination. The results are compared successfully with theoretical predictions on the three first harmonics of a periodic signal in a high degree of accuracy, when the effects of the thermoviscous dissipation and of the non-linear propagation have the same order of magnitude.

Document Type: Research Article

Publication date: 2000-09-01

More about this publication?
  • 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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