Finite-Amplitude Standing Waves in Rigid-Walled Tubes
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Authors
Coppens, Alan B.
Sanders, James V.
Subjects
Advisors
Date of Issue
1980-07
Date
Publisher
Acoustical Society of America (ASA)
Language
Abstract
A perturbation expansion is formulated for the one‐dimensional, nonlinear, acoustic‐wave equation with dissipative term describing the viscous and thermal energy lossesencountered in a rigid‐walled, closed tube with large length‐to‐diameter ratio. The resulting set of iterative, linear equations is solved for a finite‐amplitude standing wave.Solutions lead to a steady‐state distribution of harmonics of the fundamental, the amplitude and phase of each term being strong functions of frequency and the absorptive process. Necessary features of the approach include characterizing all absorptive processes by a bulk absorption coefficient and requiring a boundary‐layer depth much less than the tube diameter. The solution, while strictly limited to the preshock régime, can be used to predict certain features of the onset of shock. Intense longitudinal standing waves were generated within a rigid‐walled tube of 6‐ft length and 212‐in. diam. The tube contained air, at ambient pressure and temperature, which was excited into vibration by a piston at one end. A microphone at the rigid end of the tube was used to observe the pressure as a function of time. For input frequencies around either the fundamental or the first overtone of the tube, the amplitudes of the second and third harmonics of the finite‐amplitude wave were in excellent agreement with the predictions of the theory. Waveforms reconstructed from the predicted amplitudes and phase angles of the solution compared very well with the observed microphone output. An extension of the theory to the shock régime provided qualitative agreement with observations of the frequency dependence of both the intensity needed to produce shock and the phase of the onset of shock.
Type
Article
Description
The article of record as published may be found at https://doi.org/10.1121/1.1910860
Series/Report No
Department
Physics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funding
Format
14 p.
Citation
Coppens, Alan B., and James V. Sanders. "Finite‐Amplitude Standing Waves in Rigid‐Walled Tubes." The Journal of the Acoustical Society of America 43.3 (1968): 516-529.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.