## 4 Discussion  
As is generally known, the attenuation of the ultrasonic wave propagating in the material of the tested samples in the grains and at their boundaries increases with increasing transducer frequency and therefore with decreasing wavelength in the material structure. This explains and indicates the significant (step) increase in measurement error at high frequencies (20 MHz), as well as that most likely at higher frequencies not considered in this paper. The frequencies of the probes used in the range from several to 12.5 MHz caused a measurement error of 10-12%. Thus, the frequency of several megahertz transducers used in industrial measurements should not generate excessive errors caused by the attenuation of the ultrasonic wave in the material structure of the tested elements. On the other hand, in regard to the contribution to the weakening of the ultrasonic wave of attenuation which is not structural, but rather dependent on the state and roughness of the surface of the so-called reflector, i.e., the reflecting surface of the wave, we found that an increase in its roughness (expressed by the value of Ra) nevertheless causes a weakening of the wave. This requires amplification of its pulse by the decibel amplification system of the ultrasonic defectoscope. The phenomenon of unstructured wave attenuation noticeably increases above Ra = 50 \(\upmu\)m. This weakening of the wave is caused by the scattering of the wave on the micro-roughness of the reflector surface. The ratio of the wavelength to the size (height) of the micro-roughness of the substrate can be a quantifiable value determining the intensity of scattering. Our studies (Figure 8, Table 2) show that if this ratio tends towards 1, the attenuation caused by wave scattering on the reflector's micro-roughness increases. Thus, not only the frequency of the ultrasound source (probe), but also the size of the micro-roughness of the surface of the tested elements, from which the ultrasonic wave is reflected, can lead to errors in ultrasonic measurements. The velocity of ultrasonic waves propagating in the material of the tested element is influenced by the hardness of the material. The mechanism of this influence is explained in various ways in the literature. It is presented that this velocity increases with an increase in the tempering temperature of hardened steel samples, and therefore with a decrease in the hardness of the samples [24]. In our measurements, we found that a sample with a higher intrinsic hardness (57 HRC) had a higher propagation velocity of the longitudinal ultrasonic wave than a sample with a lower hardness (32 HRC). The metallographic structure of the sample material is responsible for its hardness. After hardening (without tempering), it is a  
Figure 10: Courses of the decibel gain difference of longitudinal ultrasonic wave pulses depending on the frequency of transducers generating it for tested hardnesses (57 and 32 HRC) of steel samples. martensitic structure with residual austenite. This structure is hard, packed, and stressed, and is responsible for the velocity of ultrasonic wave. The heating of an element in a machine or technical device in the temperature range equivalent to tempering can cause a change in the hardness of the structure and the stress state, and the reconstruction of this structure towards tempering martensite and sorbite. Then, the velocity of the ultrasonic wave will change depending on the structural and crystallographic reconstruction of the structure of the tested real machine element. Taking into account the possible limited access to the mounted element, it seems more probable that the ultrasonic wave velocity will be more dispersed than its attenuation, because the scattering of the ultrasonic wave from an inaccessible reflecting surface (reflector) has lower values in a large range of its microroughness for a given steel hardness (Figures 5-7). Measuring the speed of an ultrasonic wave with an unknown exact thickness is virtually impossible.