## 4 Results and Discussion  
### Acoustic Attenuation along Exposed MDPE Pipe  
Figure 5a,b shows the measured acoustic signals at the accelerometers located at 0 degrees around the circumference of the MDPE pipe in Figure 2. Figure 5a shows the measured acoustic signal at 0 m from the vibration motor while Figure 5b shows the measured acoustic signal at 4 m from the vibration motor. It should be noted that these measurements were taken independently, hence the acoustic pulse locations in the figures are not indicative of the measurement distances. Figure 6 further shows the frequency domain acoustic signal measured at the accelerometer located at 4 m from the vibration motor. Figure 5: Time domain acoustic signal measured at (**a**) 0 m from the acoustic transmitter and at 0 degrees around the pipe circumference and (**b**) 4 m from the acoustic transmitter and at 0 degrees around the pipe circumference. Figure 5a,b shows diminished acoustic signal amplitudes at increased distances along the exposed MDPE pipe, which is indicative of acoustic wave attenuation along the pipe. The acoustic signal at 0 m is also significantly noisier, suggesting the presence of high-frequency non-propagating acoustic wave modes generated at the point of acoustic excitation along the pipe (as noted for example in [26]). As expected, the measured acoustic signals along the pipe have peak amplitudes (during acoustic excitation of the pipe) outside the 100-200 Hz bandwidth. Table 2 and Figure 7 further show the average acoustic signal-to-noise ratios (SNR) measured at each axial distance from the acoustic transmitter and at each circumferential position around the MDPE pipe. From Figure 7, the acoustic SNR is highest when the closest to the acoustic transmitter before a significant drop in SNR between 0 and 2 m from the acoustic transmitter and a gradual SNR decrease beyond 2 m. As noted by [19], one feature of acoustic wave excitation at a single location along a pipe is the generation of high-frequency acoustic wave modes which rapidly decay from the acoustic wave source. The region between 0 and 2 m thus represents an acoustic near field where high-frequency (>1 kHz) acoustic waves (which constitute a significant portion of the acoustic energy in this region) are rapidly attenuated. Beyond 2 m (the acoustic far field), the acoustic energy is dominated by low-frequency (<1 kHz) acoustic wave propagation which gradually attenuates at increasing distances along the pipe. The average acoustic attenuation along the pipe, i.e., the change in SNR (dB) between 0 and 6 m per unit distance along the MDPE pipe, for each circumferential location around the pipe, is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Axial Distance from** \\ **Acoustic Transmitter (m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Average SNR at** \\ **0 Degrees around Pipe** \\ **(dB)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Average SNR at** \\ **90 Degrees around Pipe** \\ **(dB)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Average SNR at** \\ **180 Degrees around Pipe** \\ **(dB)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Average SNR at** \\ **270 Degrees around Pipe** \\ **(dB)** \\ \end{tabular} } \\ \hline
0 & 29.1 & 34.9 & 28.8 & 33.2 \\
2 & 25.6 & 28.2 & 24.9 & 25.6 \\
4 & 24.5 & 24.3 & 24.2 & 24.8 \\
6 & 24.2 & 24.2 & 24.2 & 24.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average SNR (dB) at each circumferential position around and axial distance along the exposed (empty) MDPE pipe. Figure 6: Frequency domain acoustic signal measured at 4 m from the acoustic transmitter and at 0 degrees around the pipe circumference. From Table 3, the average acoustic attenuation along the exposed (empty) MDPE pipe was calculated as 1.2 \(\pm\) 0.5 dB/m.