## 5 Conclusions  
This paper presented a low-frequency (<1 kHz) acoustic signal propagation system for reliable digital communication along exposed and buried MDPE pipes. Results from analytical and numerical models were compared to experimental measurements for examining acoustic signal attenuation. It was shown that the existing analytical model does not accurately predict the signal attenuation as it cannot replicate the non-axisymmetric signal generated by the ERM. Thus, it is not suitable for the prediction of the maximum reliable signal transmission. In contrast, the numerical model (with an acoustic attenuation prediction of 1.2 dB/m) showed good agreement for the acoustic signal attenuation with the experimental measurements along an exposed MDPE pipe as it considers the effect of acoustic signal dispersion along the pipe wall (in addition to pipe wall material losses) in contributing to overall acoustic attenuation along the pipe. For the buried MDPE pipe, changes in the bulk modulus of the surrounding soil (within the range evaluated) did not affect acoustic attenuation prediction along the pipe. However, it demonstrated that acoustic signal scattering from pipe wall discontinuities and acoustic-shear-wave-controlled radiation from the pipe into the soil have a significant impact on the acoustic signal attenuation. The latter is not captured in the numerical model. The numerical model showed an increased acoustic attenuation prediction of 2.1 dB/m for a finite-length pipe of 6 m length compared to the predicted acoustic attenuation of 1.5 dB/m for an infinitely long pipe. The measured acoustic attenuation of 4.7 dB/m along the 6 m buried MDPE pipe confirmed that the surrounding soil has a significant impact the overall acoustic attenuation.  
The results were also used to predict the maximum ranges at which reliable digital communication can be achieved along the pipes using the bit error rate (BER). Based on the theoretical BER predictions, it is estimated that reliable digital communication can be achieved at maximum distances approaching 18 m and 11 m along exposed and buried MDPE pipes, respectively. The findings clearly demonstrate the potential of using acoustic signal transmission between sensor nodes which fulfil the requirements of low power, small size and low cost. This can overcome the limitations of RF signal transmission, thereby reducing the number of nodes needed to transmit data between sensing nodes. Based on the results, a 40% reduction in the number of nodes for a buried MDPE pipe can be achieved compared to the number of nodes required for RF signal transmission (using commercially available radio-based data communication nodes).  
Conceptualization, D.C., N.M. and O.F. methodology, O.F.; software, O.F.; validation, O.F. and C.A.; formal analysis, O.F.; investigation, O.F.; writing--original draft preparation, O.F.; writing--review and editing, N.M., C.A. and D.C.; supervision, N.M., D.C. and C.A.; project administration, D.C.; funding acquisition, D.C. and N.M. All authors have read and agreed to the published version of the manuscript.  
The research obtained funding support from the School of Engineering providing a partial stipend for the postdoctoral research.  
Not applicable.  
The experimental and numerical data generated during this study are available on request.  
The authors would like to thank the team from the Assessing the Underworld (ATU) project for enabling the field trial, the technicians in the civil laboratory at the University of Birmingham for enabling the above ground trial and [PERSON] for helping with the formatting of the paper.  
The authors declare no conflict of interest.