## 2 Materials and Methods  
The measurements were conducted in a laboratory. The system was modelled to test the parameters of the acoustic wave propagating in a typical propagation medium such as mineral oil or ester, which are used in the insulation systems of power transformers. A piezoelectric transducer (disc type PRYY+0354, material type PIC255 [26]) was applied as the AE source and a spherical hydrophone type 8105 [27] was used as the AE receiver. Standard AE measuring apparatus was used for signal registration. The signals propagated in a plastic tank of the following dimensions: 187 mm wide, 147 mm high and 1000 mm long. The tank was filled with the considered dielectric liquids, details of their physical properties are given in Table 1. A detailed description of the measuring setup and parameters of the applied transducers is given in previously published work [22]. A scheme diagram of the experimental setup is depicted in Figure 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Property**} & **Density** & **Viscosity** & **Water content** & **Breakdown Voltage (kV)** \\  & **at 20 °C (g/cm\({}^{3}\))** & **at 40 °C (mm\({}^{2}\)/s)** & **Water content** & **Wide (kV)** \\ \hline Test method & ISO 3675 & ISO 3104 & IEC 60814 & IEC 60156/ASTM \\  & & & D877/IEC 60296 \\ Natural ester & 0.92 & 37 & 50 (mg/kg) & \(\geq 30\) \\ Synthetic ester & 0.97 & 29 & 50 (mg/kg) & \(\geq 75\) \\ Mineral oil & 0.87 & 9.9 & 50 (m/m) & \(\geq 69\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the considered dielectric liquids [23; 24; 25]. Figure 1: Scheme diagram of the experimental setup. The measuring procedure involved 2 tasks: (1) investigation of frequency modulated AE signals, in particular, values up to 400 Hz were considered. AE waves up to 400 kHz were generated and recorded, but values above 400 Hz were not detectable, and so were therefore not included in this paper. The frequency range presented was a result of hardware limitations, and (2) an investigation of the influence of distance between the transducers in the range from 2.5 cm to 82.5 cm. Within the first task, the frequency modulated AE signal was emitted at a constant location, in a series of 32 samples for each of the regarded frequency values. Within the second task, the AE signal was registered with a sampling frequency of 250 MHz at various distances to the source. The AE velocity was calculated as quotient of the distance between the measuring devices and the time of arrival \(t_{\mathrm{a}}\) values. An exemplary AE waveform generated at frequency \(f=150\) Hz is depicted in Figure 2. An exemplary AE waveform measured by a hydrophone at distance \(d=82.5\) cm and frequency \(f=150\) Hz is depicted in Figure 3. In Figure 3, the vertical line shows the value of \(t_{\mathrm{a}}\). Figure 3: Exemplary AE waveform measured by hydrophone at distance \(d=82.5\) cm and frequency \(f=150\) Hz. Figure 2: Exemplary acoustic emission (AE) waveform generated at frequency \(f=150\) Hz. (see Figure 4), while they change more dynamically in the natural ester (see Figure 5) and in the mineral oil (see Figure 6). From Figures 4-6, it can also be seen that the highest velocities registered were for the greatest frequencies and the smallest distances between the AE source and sensor location. The values reached 1785 m/s for the synthetic ester, 1730 m/s for the natural ester and 1693 m/s for mineral oil. Contrary to this, the lowest values were registered at the smallest modulation frequencies, but at various distances between the emitter and receiver. In these cases, the AE wave propagated at 1132 m/s in synthetic ester, 1133 m/s in natural ester, and 1102 m/s in mineral oil. In Figure 7, corresponding results depicting the velocity values in function of generation frequencies are presented. In Figure 8, detailed results depicting the median velocity values calculated for the AE waveform generated in the considered dielectrics, in function of distance between the emitter and receiver, are shown.