## 4 Physical Experiment
### Physical Experiment Measurement Results
#### 4.2.2 Sound Measuring Results
This is due to the distance r measured from the microphone to the damage location (Equation (6)); it is difficult to measure accurately until the damage recurs, the rolling  
The video recording showed that the sound recording was started earlier than the train passed, 5.617 s earlier than when the ATLAS LG system started registering the data, so the first two defects (wheelsets 69-71) were registered at the time mark of 23.355 and 24.079 s of the recording, and the other two (wheelsets 85 and 87) at the time mark of 27.73 and 28.59 s. Extracts of the recording are given in Figure 7 (23 to 25 s) and Figure 8 (27 to 29 s). Our goal is to determine the dependence of the magnitude of the change in sound power on the size of the defect--that is, to determine the defect parameter (size) that can be filtered by the repetition period. Figure 6: Changes in sound pressure over time. Figure 7: Measured sound pressure of 69 and 71 wheelset failure. Area 1 indicates the defect (Figure 6). Using filters based on possible recorded/detected damage (Table 5), two sound pressures peaks (SPP) were detected for each damage. The results are presented in the Table 6.  
Registered sound pressure data of wheelset 69, (based on ATLAS LG readings) have a maximum force of \(F\) = 364.13 kN and \(F_{r}\) = 469.71 kN. Registered sound pressure data of wheelset 71, (based on ATLAS LG readings) have a maximum force of \(F\) = 307.84 kN and \(F_{r}\) = 414.08 kN. Registered sound pressure data of wheelset 85, (based on ATLAS LG readings) have a maximum force of \(F\) = 300.29 kN and \(F_{r}\)= 407.38 kN. Registered sound pressure data of wheelset 87, (based on ATLAS LG readings) have a maximum force of \(F\) = 323.61 kN and \(F_{r}\) = 427.04 kN. Because the measurements were taken at a distance of 2.5 m, and the reference sound pressure is the average measured pressure, equal to 4.5 Pa, from the Equation (8) we get  
\[L_{p}=10\log_{10}\left(\frac{P}{P_{ref}}\right). \tag{9}\]  
and the sound pressure change level \(L_{p}\) is calculated. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Wheelset** & **Time** & **Pressure** \\  & **t, s** & **P, Pa** \\ \hline
69 & 23.3555 & 15.65 \\  & 23.5703 & 11.50 \\  & 24.0820 & 11.71 \\
71 & 24.2871 & 13.83 \\  & 27.738 & 5.76 \\
85 & 27.967 & 8.5 \\
87 & 28.54 & 7.58 \\  & 28.81 & 12.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of sound pressure measurements. Figure 8: Sound pressure due to the 85 th and 87 th wheelset defects. Area 2 indicates the defect (Figure 6). Sound power change level \(L_{w}\) in the source is calculated using the equation derived from Equation (6):  
\[L_{w}=L_{p}+\left|10\log\!\left(\frac{Q}{4\pi r^{2}}\right)\right|. \tag{10}\]  
In the Tables 3 and 7, we can see that the results of the experiment differ two-fold from the theoretical calculations. This suggests that the article in preparation for the theoretical model ([PERSON] and [PERSON] [11]) contains a mistake, and instead of Equations (4), (5) and (7), the following equations should be used:  
\[L_{w}=20\log_{10}\!\left(\frac{W}{W_{ref}}\right); \tag{11}\]  
\[L_{w}=20\log_{10}\!\left(\frac{F}{F_{ref}}\right); \tag{12}\]  
\[L_{p}=20\log_{10}\!\left(\frac{P}{P_{ref}}\right). \tag{13}\]  
The recalculated results using the equations noted are given in Table 8.  
Comparing Tables 7 and 8, we can see that the results are very similar. As noted previously, the aim of our work is to determine the magnitude of sound pressure changes due to damage and its dependence on its magnitude. Knowledge of vertical force is used as confirmation of the reliability of a mathematical model and measurement results. As we can see from the results, Equations (4), (5) and (7) in the mathematical model need to be changed to Equations (11)-(13); moreover, more microphones are needed to obtain more reliable results. From the diagrams given in Figures 7 and 8, we can see that for each defect only two sound pressure change peaks were registered.