JAMC

Article http://dx.doi.org/10.26855/jamc.2026.06.002

New Theory of Resonance of an Acoustic Tube by Equivalent Transmission Circuit

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Takayoshi Nakai

Department of Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Chuo-ku 432-8561, Hamamatsu, Japan.

*Corresponding author:Takayoshi Nakai

Published: May 29,2026

Abstract

This paper describes a study on the resonance of acoustic tubes. For an air column tube closed at one end, when there is an external sound source, measuring the sound pressure at the open end shows that at frequencies which are odd multiples of one-quarter of the wavelength, the sound pressure becomes almost 0 Pa, and local maxima of the sound pressure appear at frequencies lower than those frequencies. Similar phenomena occur in a coffee can or a Helmholtz resonator. Therefore, using probe microphones, sound pressure inside and outside of the air column tubes and the coffee can has been measured. The sound pressure inside and outside a tube without a material attachment part for measuring the normal incident absorption coefficient has been measured. It is found that the impedance seen from the outside to the inside of the tube is different from the impedance seen from the inside to the outside of the tube. Based on them, a circuit model was made using a transmission line with a transformer, and its transfer function without end correction can be obtained. The results were in close agreement with the measurement results. Frequency characteristics of the opening of the tubes are also obtained when their bottoms are tapped.

Keywords

Air column resonance; Helmholtz resonance; transmission line; transformer; impedance seen from outside and inside tube; without end correction

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How to cite this paper

New Theory of Resonance of an Acoustic Tube by Equivalent Transmission Circuit

How to cite this paper: Takayoshi Nakai. (2026) New Theory of Resonance of an Acoustic Tube by Equivalent Transmission Circuit. Journal of Applied Mathematics and Computation, 10(2), 76-92.

DOI: http://dx.doi.org/10.26855/jamc.2026.06.002