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Analytical relationship between sound relaxational absorption and sound speed dispersion in excitable gases

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Abstract

Whether sound relaxational absorption and sound speed dispersion can be used as two independent acoustic parameters for gas sensing or not is still uncertain. In this paper, the analytical relationship between the frequency-dependent sound relaxational absorption and sound speed dispersion in excitable gases is derived and analyzed. First, the coefficient of compressibility in the Newton–Laplace equation of sound speed is extended to an effective one for relaxing gas. Second, using the relationship between the effective coefficient of compressibility and the effective wave number, we obtain the analytical relationship between sound relaxational absorption and sound speed dispersion from the high-frequency and the low-frequency sound speeds, respectively. The derivation and the simulation results for gas mixtures, including carbon dioxide, methane, and nitrogen, demonstrate that the ratio of the high-frequency sound speed to the low-frequency sound speed determines the amplitude of acoustic relaxation absorption peak, that the inflection frequency of sound speed dispersion is consistent with the relaxation frequency of sound relaxational absorption, and that sound speed dispersion contains all molecular information carried by sound relaxational absorption and is more applicable to acquiring the molecular geometry, the vibration frequency, and other gas molecular characteristics. This paper provides a more theoretical basis on using acoustic speed dispersion for gas sensing.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive and insightful comments for further improving the quality of this work. This work is supported by the National Natural Science Foundation of China (Grant nos. 62071189, 61461008, 11764007), the National Science Foundation of Guizhou Province, China (Grant no. Qian Ke He Ji Chu-ZK[2021] Yi Ban 318), the National Science Foundation of Henan Provincial Department of Science (Grant no. 212102310906), and the Recruitment Program of Guizhou Institute of Technology (Grant No. XJGC20140601).

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Authors and Affiliations

  1. College of Artificial Intelligence and Electrical Engineering, Guizhou Institute of Technology, Guiyang, 550003, China

    Kesheng Zhang & Shigong Zhang

  2. Faculty of Intelligent Manufacturing, Wuyi University, Jiangmen, 529020, China

    Yi Ding

  3. Science and Technology on Near-Surface Detection Laboratory, Wuxi, 214035, China

    Kai Ding

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  1. Kesheng Zhang
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  2. Shigong Zhang
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  4. Kai Ding
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Correspondence to Kai Ding.

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Zhang, K., Zhang, S., Ding, Y. et al. Analytical relationship between sound relaxational absorption and sound speed dispersion in excitable gases. J. Korean Phys. Soc. 78, 1038–1046 (2021). https://doi.org/10.1007/s40042-021-00158-3

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