## 6 Conclusions  
The wavelength in water becomes longer with the frequency decreasing, which cause it is difficult to measure and remove the reflected wave from the end of the sound tube with traditional methods, so the reflection coefficient and transmission coefficient of the underwater material at low frequencies cannot be accurately measured. However, The adaptive algorithm in this paper can effectively remove the transmission-reflected waves at low frequencies, and accurately measure the reflection coefficient and transmission coefficient of the test sample. This work proves that the adaptive control termination of an sound tube can help form traveling waves downstream of the tube, and the reflection and transmission coefficients of sample can be calculated automatically and accurately. It confirms the achievable line of the theory from three steps: theory, simulation, and experiment.  
First, adaptive control theory of a transmission sound field is proposed through the analysis of the characters of an impedance tube and research on the LMS algorithm.  
Second, a physical model that conforms to a real impedance tube is built in the COMSOL simulation software, and a real intratube environment is simulated. The acoustic information of the inner part of the sound tube is extracted before and after control using the adaptive method. The successful establishment of transmission-traveling waves downstream of the tube is proven through comparing the sound field downstream of the impedance tube between control on and off. The effectiveness of the adaptive method is also verified.  
Lastly, the experimental results demonstrate that transmission-traveling waves are formed successfully by extracting the sound pressure information of four hydrophones downstream of the impedance tube. The trend of the curve of the reflection and transmission coefficients of the sample calculated using a computer is consistent with the theoretical curve, with a minor difference.  
The advantage of the TWT adaptive control method over the transfer function method includes that the adaptive control method can avoid multiple repetitive operations while changing the test frequency. Moreover, the reflection and transmission coefficients of the sample can be calculated simultaneously through the adaptive control system, and the absolute error of the measurement result is less than 0.02. By contrast, the transfer function method cannot do it.  
Methodology, Y.X., X.Z.; software, X.Z.; validation, Y.X.; formal analysis, Y.X.; writing--original draft preparation, Y.X.; writing--review and editing, X.Z., Y.X.; supervision, Y.X. All authors have read and agreed to the published version of the manuscript.  
This research work was funded by Natural Science Foundation of Heilongjiang Province (LH2020A009).  
Figure 18: Comparison of the theoretical, the simulation values and experimental values of reflection coefficient (R) and transmission coefficient (T), when there is a steel sample in the impedance tube.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors would like to thank the College of Underwater Acoustic Engineering Laboratory.  
**Conflicts of Interest:** The authors declare no conflict of interest.