## 4 Simulation
### Procedure for Forming a Transmission-Traveling Wave Field
The distance between hydrophones and the distance from hydrophones to the surface of sample are shown in Table 1. When the test frequency range is 100-750 Hz, selecting hydrophones 2, 3, 6, and 7 as the signal input of the adaptive system, and for the test frequency range is 750 to 2500 Hz, the combination selected is hydrophones 1, 2, 7, and 8. First, we control a waveform generator (Agilent 33210A) to generate a continuous plane wave signal with certain frequency and amplitude, which is amplified using a power amplifier (B&K 2713) to excite the primary sound source. Then, the acoustic pressure information detected using the six hydrophones after passing through the measurement amplifier (B&K 2694) is transferred into a digital signal processing (DSP) board. The acoustic pressure signal amplified using hydrophones 3 and 4 is sent into the adaptive control algorithm in the DSP board to compute the proper exciting signal to cancel the transmission-reflection wave (D). The adaptive algorithm implemented in the DSP board can be programmed in the code composer studio (CCS) software on a computer. The outputs of the six hydrophones, set as the inputs for the DSP board and their sound pressure information, can be displayed in the CCS of the computer. When the output of the secondary source is kept stable, the computer collects the acoustic pressure information of the four hydrophones downstream again to observe the ideal degree of the transmission-traveling wave field. The output amplitude of the waveform generator is set as 1 Vpp, the amplification of the power amplifier (B&K2713) is set as 40 dB, and the amplification of the measurement amplifier (B&K2694) is set as 10 dB. The primary and secondary sound sources are self-developed products of the same type which the resonant peak is about 30 kHz. The transmission voltage response is relatively flat in the experimental test frequency range 100 to 2500 Hz. In the test frequency range, when the test frequency is changed, the error function of the adaptive algorithm will minimize to 1 Pa in 5 s. Once the amplitude of error signal tends to zero and remains stable, collecting the sound field information in the tube. In this experiment, the threshold of the amplitude of error signal is set at 1 Pa. The relationship between acoustic pressure amplitude and phase and sound tube length in the frequency of 600 Hz is shown in Figures 15 and 16. When a transmission-traveling wave is formed, the reflection coefficient (R) and transmission coefficient (T) will be obtained in accordance with Equations (7) and (8). The results are displayed in Figures 17 and 18. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Distance** & \(\mathbf{l_{12}}\) & \(\mathbf{l_{23}}\) & \(\mathbf{l_{34}}\) & \(\mathbf{S_{1}}\) & \(\mathbf{d  
Figure 16: (**a**) The relationship between acoustic pressure amplitude and impedance tube length with steel sample at 600 Hz. (**b**) The relationship between acoustic phase and impedance tube length with steel sample at 600 Hz. Figure 5:0 Comparison of the theoretical, the simulation values and experimental values of reflection coefficient (R) and transmission coefficient (T), when there is no sample in the impedance tube. Figure 5:1 (**a**) The relationship between acoustic pressure amplitude and impedance tube length without sample at 600 Hz. (**b**) The relationship between acoustic phase and impedance tube length without sample at 600 Hz.