## 3 Experimental Apparatus and Procedure  
To verify the theoretical results, experiments were carried out using the system shown in Figure 2. These experiments focused on the distribution of the sound field and the acoustic propagation behavior in the pipeline for different excitation sources when the liquid in the pipeline was stationary. The experimental conditions are listed in Table 2, and photographs of the experimental conditions and experiment apparatus are shown in Figure 3.  
Normal waves in the pipeline can be analyzed under white noise conditions. The white noise frequency range was selected as 0-20 kHz according to the sampling frequency of the collector and the theoretically calculated normal frequency. The variation of the sound field along the axial direction in the pipeline can be analyzed under a single-frequency-signal condition. The two frequencies below and above the cutoff frequency were selected in experimental conditions 2 and 3, respectively, to verify the cutoff effect of the sound in the pipeline. Single-frequency mechanical excitation corresponds to the acoustic signal experimental conditions, and the propagation path of the sound was analyzed along the axial direction, and therefore experimental conditions 4 and 5 involved transmission of two single-frequency mechanical force signals of the same frequency as the sound source. The maximum sampling rate of the B&K pulse collector was 131,072 Hz. The sensors used in this experiment were a B&K8103 hydrophone and B&K4371 vibration sensor. Their specifications are given in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Condition** & **Source** & **Frequency (kHz)** & **Remarks** \\ \hline
1 & White noise signal & 0–20 & \\ \hline
2 & Single-frequency acoustic signal 1 & 4.2 &
\begin{tabular}{c} Single-frequency signal below the cutoff frequency \\ \end{tabular} \\ \hline
3 & Single-frequency acoustic signal 2 & 5.2 &
\begin{tabular}{c} Single-frequency signal above the cutoff frequency \\ \end{tabular} \\ \hline
4 & \
\begin{tabular}{c} Single-frequency mechanical signal 1 \\ \end{tabular} & 4.2 &
\begin{tabular}{c} The excitation point is outside the tube \\ wall, directly below the sound source \\ \end{tabular} \\ \hline
5 & \
\begin{tabular}{c} Single-frequency mechanical signal 2 \\ \end{tabular} & 5.2 &
\begin{tabular}{c} The excitation point is outside the tube \\ wall, directly below the sound source \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental conditions. Figure 3: Experimental apparatus and acquisition system: (**a**) B&K2713 power amplifier; (**b**) YE5859 charge amplifier; (**c**) B&K pulse collector; (**d**) Agilent 33522A signal source; (**e**) hydrophone bracket; (**f**) experimental acquisition system. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Hydrophone (B\&K\$103)** \\ \hline Voltage sensitivity & Frequency range & Maximum operating static pressure \\ \hline
30 \(\mu\)V/Pa & 0.1–180 kHz & 4 \(\times\) 10\({}^{6}\) Pa \\ \hline  & Vibration sensor (B\&K\$371) \\ \hline Charge sensitivity & Frequency range & Maximum operational level \\ \hline
1 pC/ms\({}^{2}\) & 0.1–25 200 Hz & 6000g \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specifications of sensors. Figure 2: Experimental system for investigating acoustic propagation characteristics of a fluid-filled PE pipeline. As mentioned in references [10; 11; 12; 13], there have been many experimental investigations of acoustic propagation in fluid-filled elastic pipelines; however, these pipelines were rather short, and there was no special treatment of the end of the pipeline other than, in some cases, the simple addition of a flange, which caused inverse superposition of the sound field in the axial direction. These previous experiments used a single hydrophone, measuring the sound pressure spectrum at a single point only, and therefore it was not possible to obtain the distribution of the sound field along the entire pipeline.