## 1 Introduction
They performed modal and transient piezoelectric analysis to determine the eigenmodes and frequencies of the system that were used to investigate the harmonic wave propagation characteristics of the system. [PERSON] and [PERSON] [10] conducted a series of numerical studies using FEA to investigate the wave propagation behaviour in wooden poles. Their results showed that a higher elastic modulus in longitudinal direction always generated higher guided wave behaviour in a wooden pole, and experimental testing was performed to validate their findings. Many works have been conducted with the aim of improving the computational efficiency and accuracy of the convectional FEA method. [PERSON] and [PERSON] [11] investigated the effect of leakage on acoustic wave propagation in an air-filled pipe using the FEA method and experimental testing. Their predicted and measured data was subsequently used to identify and locate the leakage using a Time-of-Flight approach. Other numerical techniques have been used for predicting acoustic wave propagation. These include the Boundary Element Method (BEM), Statistical Energy Analysis (SEA), and the SWAN (Simulating Waves Nearshore) spectral phase averaged wave model. For example, [PERSON] et al. [12] used the Finite Element Method and Boundary Element Method (FEM-BEM) to analyse acoustic fluid-structure interaction. An algorithm based on FEM-BEM was presented for simulation of fluid-structure interaction in their work. The accuracy of the simulation was improved by evaluating the single integrals in boundary integral equations using the Cauchy principal value and the Hadamard finite part integral method. In order to understand the mechanism of acoustic wave propagation in a body, the noise propagation in ship structures was investigated by [PERSON] et al. [13], and was tested in several vessels using Statistic Energy Analysis (SEA). Their predicted result was compared with the experimental results obtained from tests carried out using similar vessels. [PERSON] [14] studied the patterns by which wave energy propagates in the western side of the Black sea and simulated the propagation using the SWAN spectral phase averaged wave model. The study shows that there is a tendency for the waves to travel faster along the Black sea surface. A field experiment to assess the feasibility of using commercially available accelerometers and related signal condition to analyse acoustic wave propagation in a pipe was recently conducted [15]. Results from the experiments confirmed that attenuation is the most important factor that affects the viability of acoustic wave propagation for impact detection. In another work, a sound intensity measurement technique was used to investigate how sound energy propagates around organ pipes [16]. The authors obtained the sound intensity distributions around the pipes, and the directions of the acoustic energy flow were presented. [PERSON] et al. [17] used the acoustics pulse reflectometer technique for flaw detection in pipes in the time domain. The use of analytical equations to investigate acoustic- or pressure-wave propagation in a fluid-filled pipeline might be straight-forward and easily implemented for a simple straight pipe. However, when pipe networks are involved, the prediction of acoustic or pressure wave propagation becomes very difficult to implement analytically. In such cases, the use of a numerical method, such as FEA, is imperative. However, large errors may also occur in the numerical predictions of acoustic wave propagation. For example, when FEA was used to predict acoustic wave propagation in an air-filled pipe, as in the work by [PERSON] and [PERSON] [11], very large acoustic speed errors were obtained. They used 3D hexahedral acoustic elements whose structural counterparts usually give accurate predictions. They expected the 3D hexahedral acoustic elements to also give accurate predictions, but did not check to confirm the degree of their accuracy.