進行水下材料聲學特性的量測時，管內聲速與聲波衰減常數是重要參數，但目前多使用理論值而缺乏實際量測。本研究探討充水阻抗管中波傳參數的量測方法，並提出一種結合迭代式傳遞矩陣法與非線性約束優化法之波傳參數估測技術，可大幅提升管內聲速與衰減常數的估測準確度。研究中利用COMSOL有限元素軟體建立具聲固耦合與黏滯效應之充水阻抗管模型，並分析不同終端邊界條件與水聽器數量對於波傳參數估算的影響。本研究依照數值模型建立等比例的雙腔室充水阻抗管實體，進行波傳參數與材料正向吸音係數量測，實驗中評估不同方法(振幅匹配法、單次與兩次量測法、標準與非線性約束優化法)於估算複數波數的準確性與穩定性。
結果顯示，非線性約束優化法能有效克服標準方法在釋壓邊界條件下的奇異值問題，經由結合多支水聽器與兩次量測能更進一步降低雜訊干擾，提升量測精確度。本研究另針對單頻音與白噪音作為聲源進行量測效率與準確性的比較，結果指出白噪音雖可有效縮短量測時間，但穩定性不及單頻音。最後，將本研究提出之非線性約束優化法應用於雙腔室充水阻抗管之材料吸音量測上，結果顯示該方法搭配兩次量測的評估結果最合理，並且與單腔室充水阻抗管之三參數校正法結果最為接近。

Accurate estimation of sound speed and attenuation in water-filled tubes is crucial for underwater acoustic material characterization; however, most methods rely on theoretical values without experimental validation. This study presents a measurement approach utilizing a dual-cavity water-filled impedance tube to determine complex wavenumbers and absorption coefficients. A COMSOL-based finite element model, which incorporates fluid-structure interaction and viscous effects, is employed to examine the impact of boundary conditions and hydrophone configurations. Various methods, including amplitude matching, one-load and two-load techniques, as well as both standard and nonlinear constrained optimizations, are evaluated. The nonlinear constrained method effectively overcomes the singular value problem of the standard method under pressure-release boundaries and enhances wavenumber accuracy. In addition, the nonlinear constraint optimized two-fold measurement method with multiple hydrophones can significantly reduce the noise interference and improve the measurement accuracy. Results indicate that neglecting wave attenuation leads to overestimated absorption. Furthermore, while white noise shortens measurement time, single-frequency excitation yields more stable results. The dual-cavity water-filled impedance tube was used to measure the acoustic absorption coefficient of the material, and it was found that the results of the nonlinear constraint-optimized two-load method were closest to those of the three-parameter calibration method.

[1]. ASTM C384-90a, “Standard test method for impedance and absorption of acoustical materials by the impedance tube method,”1998.
[2]. ASTM E 1050-98, “Standard test method for impedance and absorption of acoustical materials using a tube, two microphones and a digital frequency analysis system,”1998.
[3] ASTM E2611-19, “Standard test method for normal incidence determination of porous material acoustical properties based on the transfer matrix method,” ASTM International, West Conshohocken, PA, 2019.
[4] A. F. Seybert and D. F. Ross, “Experimental determination of acoustic properties using a two‐microphone random‐excitation technique,” The Journal of the Acoustical Society of America, vol. 61, pp. 1362–1370, 1977.
[5] J. Y. Chung and D. A. Blaser, “Transfer function method of measuring in‐duct acoustic properties. I. Theory,” The Journal of the Acoustical Society of America, vol. 68, pp. 907–913, 1980.
[6] J. Y. Chung and D. A. Blaser, “Transfer function method of measuring in‐duct acoustic properties. II. Experiment,” The Journal of the Acoustical Society of America, vol. 68, pp. 914–921, 1980.
[7] A. F. Seybert and B. Soenarko, “Error analysis of spectral estimates with application to the measurement of acoustic parameters using random sound fields in ducts,” Journal of the Acoustical Society of America, vol. 69, pp. 1190–1199, 1981.
[8] H. Bodén and M. Åbom, “Influence of errors on the two‐microphone method for measuring acoustic properties in ducts,” The Journal of the Acoustical Society of America, vol. 79, pp. 541–549, 1986.
[9] B. H. Song and J. S. Bolton, “A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials,” The Journal of the Acoustical Society of America, vol. 107, pp. 1131–1152, 2000.
[10] M. E. Delany and E. N. Bazley, “Acoustical properties of fibrous absorbent materials,” Applied Acoustics, vol. 3, pp. 105–116, 1970.
[11] P. Bonfiglio and F. Pompoli, “A single measurement approach for the determination of the normal incidence transmission loss,” The Journal of the Acoustical Society of America, vol. 124, pp. 1577–1583, 2008.
[12] S. S. Corbett and A. D. Stuart, “A two-hydrophone technique for measuring the complex reflectivity of materials in water-filled impedance tubes,” The Journal of the Acoustical Society of America, vol. 77, pp. S58–S58, 1985.
[13] P. S. Wilson, R. A. Roy, and W. M. Carey,“An improved water-filled impedance tube,” The Journal of the Acoustical Society of America, vol. 113, pp. 3245-3252, 2003.
[14] M. Oblak, M. Pirnat, and Miha Boltežar, “An impedance tube submerged in a liquid for the low-frequency transmission-loss measurement of a porous material,” Applied Acoustics, vol. 139, pp. 203–212, Oct. 2018.
[15] V. A. Del Grosso, “Analysis of Multimode Acoustic Propagation in Liquid Cylinders with Realistic Boundary Conditions–Application to Sound Speed and Absorption Measurements,” Acta Acustica united with Acustica, vol. 24, pp. 299-311, 1971.
[16] L. Dwynn Lafleur and F. Douglas Shields, “Low‐frequency propagation modes in a liquid‐filled elastic tube waveguide,” The Journal of the Acoustical Society of America, vol. 97, no. 3, pp. 1435–1445, 1995.
[17] 簡志宇, “以注水彈性阻抗管測量材料之水中聲學特性 之研究,” 碩士論文, 工程科學及海洋工程學研究所, 臺灣大學, 2005.
[18] J. Han, D. W. Herrin, and A. F. Seybert, “Accurate Measurement of Small Absorption Coefficients,” SAE technical papers on CD-ROM/SAE technical paper series, 2007.
[19] W. Wang, P. J. Thomas, and T. Wang, “A frequency-response-based method of sound velocity measurement in an impedance tube,” Measurement Science and Technology, vol. 28, no. 4, pp. 045007–045007, 2017.
[20] Z. Mo, G. Song, K. Hou, and J. S. Bolton, “An iterative transfer matrix approach for estimating the sound speed and attenuation constant of air in a standing wave tube,” The Journal of the Acoustical Society of America, vol. 151, no. 6, p. 4016, 2022.
[21] S. Temkin, Elements of Acoustics. John Wiley & Sons, 1981.
[22] L. E. Kinsler, Fundamentals of acoustics. New York: John Wiley & Sons, 2000.
[23] 蔡承霖, “基於單腔室阻抗管之水中材料聲學特性參數量測系統開發,” 碩士論文, 系統及船舶機電工程研究所, 成功大學, 2024.