## 3 Results of Our Own Ultrasonic Tests
### Hardness Estimation Results  
In accordance with the assumptions in the first stage of the research, the velocity of the longitudinal ultrasonic wave was measured, using the probes listed in Table 2, for samples with a hardness of 32 and 57 HRC. The average velocities obtained for all the probes used and for specimens with significantly different hardnesses are shown in Figure 9.  
Figure 8: The results of all ultrasonic measurements depending on the frequency of the ultrasonic probe and surface roughness.  
Figure 7: Values of measurement errors depending on the frequency of the ultrasonic probe.  
There were no significant differences between the velocities of the ultrasonic longitudinal wave for the different probe frequencies in the range tested, whereas there are clearly differences in the velocity of this wave for the different hardnesses of the samples tested. The higher velocity of this wave was verified by the higher hardness of the samples (57 HRC). The lower speed of the wave corresponds to the lower hardness (32 HRC). There is no convergence here, with the trend indicated in [24]. For a given hardness, the velocity differences due to the frequency of the transducers used are small. They are within the range of measurement errors. It can therefore be assumed that the influence of the head frequency on the measured velocity value is negligible.  
A significant disadvantage of ultrasonic measurements aimed, for example, at estimating the hardness of elements under industrial or operational conditions is the lack of knowledge of the thickness of the assessed element, which is necessary for the determination of velocity. In the case of built-up components, with one-sided access to them, which is often the case in practice, from an operational point of view, the attenuation of the ultrasonic wave may be a better measure of the hardness of the tested element. Also, the waveforms of the decibel difference in the amplification of the longitudinal ultrasonic wave pulses for the tested hardness of the steel samples (Figure 10), depending on the frequency  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & \multicolumn{4}{c}{**Frequency of the Ultrasonic Probe (MHz)**} \\
**Ra (\(\mu\)m)** & **2** & **2.4** & **2.75** & **4** & **9** & **12.5** & **20** \\ \hline
0.34 & 7.22 & 9.37 & 3.80 & 5.71 & 7.02 & 5.38 & 13.45 \\
1.06 & 7.38 & 9.15 & 4.22 & 6.14 & 6.72 & 6.06 & 13.18 \\
1.3 & 7.38 & 8.40 & 7.44 & 6.10 & 7.45 & 6.29 & 13.88 \\
1.36 & 7.91 & 7.86 & 6.60 & 5.82 & 7.43 & 5.57 & 14.09 \\
2.57 & 7.79 & 8.42 & 6.97 & 6.57 & 7.01 & 6.41 & 13.48 \\
0.33 & 7.70 & 8.41 & 6.51 & 6.19 & 6.71 & 5.26 & 13.28 \\
1.59 & 7.66 & 8.21 & 5.69 & 6.63 & 7.55 & 6.65 & 13.67 \\
2.27 & 7.98 & 8.76 & 5.13 & 5.78 & 7.13 & 5.94 & 13.12 \\
2.59 & 7.75 & 8.68 & 4.84 & 6.48 & 7.85 & 5.73 & 13.86 \\
50.62 & 8.16 & 9.35 & 5.82 & 6.66 & 8.95 & 6.90 & 14.17 \\
149.15 & 8.07 & 8.62 & 8.20 & 6.89 & 9.49 & 7.94 & 15.35 \\
250.73 & 8.15 & 9.32 & 10.86 & 8.28 & 9.97 & 8.64 & 17.84 \\
348.69 & 8.73 & 11.87 & 11.24 & 8.79 & 10.01 & 6.43 & 19.30 \\ \hline \end{tabular}
\end{table}
Table 3: Summary of decibel amplification values of reflected ultrasonic wave impulses depending on the height of the reflector surface micro-roughness and the frequency of the ultrasonic probes used.  
Figure 9: Distribution of the average velocities of the longitudinal ultrasonic wave for the probes used and for specimens with different hardnesses.  
of the transducers generating it, indicate their similarity for significantly different specimen hardnesses. This can make it difficult to quantify the hardness of the test pieces.