## 4 Physical Experiment
### Physical Experiment Measurement Results
#### 4.2.2 Sound Measuring Results
This is related to the distance of the device to the point of contact of the wheel defect. The rolling stock is moving, but the place of measurement is fixed. Each defect is repeated only around every 3 m, so in case it is desired to detect two sound pressure change peaks, the rolling stock must travel 6 m, and for three peaks it must travel 9 m. As we can see in Equation (6), the sound pressure depends \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Wheelset**} & **Time** & **Sound Pressure** & **Reference Sound** & **Change of Sound** & **Change of Sound** \\  & **t, s** & **\(P\), Pa** & **Pressure \(P_{ref}\), Pa** & **Pressure Level** & **Pressure Level** \\  & & & & **\(L_{p}\), dB** & **Power \(L_{w}\), dB** \\ \hline \multirow{2}{*}{69} & 23.3555 & 15.6500 & 4.5000 & 10.8260 & 23.7541 \\  & 23.5703 & 11.5000 & 4.5000 & 8.1497 & 21.0778 \\  & 24.0820 & 11.7100 & 4.5000 & 8.3069 & 21.2350 \\  & 24.2871 & 13.8300 & 4.5000 & 9.7522 & 22.6803 \\  & 27.7380 & 5.7600 & 4.5000 & 2.1442 & 16.6559 \\  & 27.9670 & 8.5000 & 4.5000 & 5.5241 & 20.0358 \\  & 28.5400 & 7.5800 & 4.5000 & 4.5291 & 17.4572 \\  & 28.8100 & 12.3300 & 4.5000 & 8.7550 & 21.6831 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Wheelset**} & **F, kN** & **\(F_{r}\), kN** & **\(F_{ref}\), kN** & **\(F_{r}\), kN** & **\(L_{w}\), dB** & **\(L_{wr}\), dB** \\ \hline
69 & 364.13 & 469.71 & 25 & 33 & 23.26633 & 23.06632 \\
71 & 307.84 & 414.08 & 25 & 33 & 21.8077 & 21.97141 \\
85 & 300.29 & 407.38 & 25 & 33 & 21.59202 & 21.82972 \\
87 & 323.61 & 427.04 & 25 & 33 & 22.24164 & 22.23909 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Corrected results for the theoretical sound power change calculation. significantly on the distance. Thus, in order to register more peaks, more microphones would be needed. Comparison of Measurements Results with the Calculations of the Mathematical Model of the Numerical Experiment. Results of the Calculations According to the Data of the Physical Experiment  
In this section, a numerical mathematical model (Petrenko and Kukenas [11]) is considered, which is obtained by considering the dependence of the change in the forces acting on the change in sound pressure as a test/check in this work by physical experiment. Calculations were made taking into account the physical experiment data of the track condition, wheelset load and speed. Maximum and reference forces were obtained. The results are presented in the Table 9 and in Figures 9-12. Figure 11: Calculated force values of the 85 th wheelset. Figure 10: Calculated force values of the 71 st wheelset. Calculations were performed according to Section 3.1, replacing Equations (4), (5) and (7) with (11)-(13), respectively. The results are presented in Table 10 and in Figures 13-16. It should be mentioned that only two sound pressure peaks (SPP) can be detected with one microphone; more microphones are needed to detect more SPP. Table 10 shows the changes in sound pressure at the source. The difference between them is 2 dB, but the existing damage within the normal range should already be repaired. Therefore, this is sufficient to detect damage. Since different countries may have different possible and forbidden damage parameters, we provide Equations (6), (12) and (13) according to which the corresponding SPP parameters can be determined. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wheelset** & \begin{tabular}{c} **Max Sound Power** \\ **Level, dB** \\ \end{tabular} & \
\begin{tabular}{c} **Min Sound Power** \\ **Level, dB** \\ \end{tabular} &
\begin{tabular}{c} **Average Sound** \\ **Power Level, dB** \\ \end{tabular} \\ \hline
69 & 22.52 & 21.30 & 22 \\ (Figure 13) & 21.26 & 20.12 & 20.77 \\ (Figure 14) & 21.7 & 20.25 & 21.39 \\ 85 & 21.7 & 20.03 & 21.17 \\ (Figure 15) & 22.07 & 20.03 & 21.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results of sound power level calculation.