## 1 Introduction
Researchers have also conducted similar investigations on a vastly different material, marble [23], using ultrasonic techniques to analyze the average grain size of certain marbles through ultrasonic velocity measurements. They successfully presented the relationship between ultrasonic velocities and grain size graphically and compared the average grain size of marble samples with microscopic images. Researchers often used ultrasonic wave velocity as a measure of hardness. It has been shown that by using additional material information, such as chemical composition and tempering temperature, high correlation can be achieved between ultrasonic wave velocity and hardness for different types of steel using multiple regression analysis [24]. Essentially, steel hardness can be predicted based on the transverse wave velocity, provided the content of only one chemical element is known. Similarly, in the study [13], the authors observed that the ultrasonic wave velocity correlates with surface hardness in isotropic materials. The results demonstrated that this technique can be considered an effective method for evaluating volumetric hardness. Destructive surface methods and non-invasive volumetric methods provide similar hardness distributions; however, the average hardness and surface hardness values differ. However, the majority of non-destructive testing carried out takes place not in laboratories, but in industrial settings. To measure the ultrasonic wave velocity with high accuracy, knowledge of the thickness of the tested element or access to both sides of the specimen or actual item is necessary. When examining material properties (e.g., hardness) in industrial conditions, there may not always be information available regarding the thickness of the tested element or access to both sides of it. Therefore, in an industrial testing, a better measure of hardness than wave velocity might be attenuation. In the present work, the level of ultrasonic wave attenuation in decibels was determined based on the difference in heights between two consecutive reflected pulses (i.e., the first and second ones) obtained on the screen of the ultrasonic flaw detector. For this purpose, measurements of the amplifier characteristics of the ultrasonic apparatus were carried out for appropriate time bases and settings (voltage, pulse width). Based on these characteristics, the level corresponding to a specific height of the reflected or transmitted pulse through the tested sample was determined in decibels. In practice, the first reflected pulse was always set at the same height. The use of the amplification characteristic eliminated errors arising from the nonlinearity of amplification depending on the range and height of the pulse observed on the screen and the pressure force of the ultrasonic transducer head on the tested surface. Another factor that may impact the results of ultrasonic testing is surface roughness [25]. The authors in their research used a 5 MHz frequency wave and employed an immersion technique. In the study [25], it was shown that the RMS height of the surface microtopography in the normal direction plays a dominant role in the amplitude of the echo signal and the shape of the surface crack wave reflector. Similar studies have been conducted by various research centers, and all the researchers concluded that the surface condition can influence the results of ultrasonic testing, including corrosion monitoring [26]. In the study [27], the authors used frequencies ranging from 2 to 20 MHz but limited the surface roughness to the range of 5 to 50 \(\upmu\)m. The authors [26] found that surface roughness significantly degraded the signal-to-noise ratio (S/N) for some typical inspection geometries. Additionally, after appropriate normalization, the transmission and reflection coefficients for the coherent beam were found to be nearly universal functions of the angle of incidence, except near the critical angles.