## 2 Characteristics of the Shock Wave and Its Sources
Due to the radial nature of the tested shock wave, different energy densities (4) are obtained at different points of the cross-section perpendicular to the wave vector, therefore the total energy measure for the cross-section \(\Phi\)[1,11], which corresponds to the shock wave passing the surface, is used based on the previous Equation (4):  
\[E_{t}(\Phi)=\frac{1}{\rho c}\int_{\Phi}\,\int_{0}^{\lambda}\,p^{2}(\xi,t)dtd\xi \qquad[] \tag{5}\]  
This seems to be the clinically more important parameter of the shock wave in case of tissue treatment. Moreover, the measure (5) is supplemented with the number of delivered shock wave pulses during the treatment or the frequency (6), with which successive pulses are delivered. Therefore, assuming the limitation of the experimental test benches consisting in the possibility of measuring the energy flux density only in one specific point \(\xi\) of the medium, the energy flux density measure (4) per point of the medium during the entire shock wave pulse is used in the following part of the study. If the shock wave pulses are generated with the frequency \(f\), then the energy flux density of one pulse at the point \(\xi\) is:  
\[E(\xi)=\frac{\sum\,E(\xi)}{f} \tag{6}\]  
where:  
\(\Sigma E\) (\(\xi\))--total energy supplied to the point \(\xi\) in one unit of time. Formula (6)--the total energy supplied to the point \(\xi\) is the product of the frequency and the energy flux density at the point \(\xi\), which seems trivial. However, in real design solutions, it turns out that the following dependence holds:  
\[E(\xi)=\frac{\sum\,E(\xi)}{k(f)f} \tag{7}\]  
where there is factor \(k\) dependent on the frequency. This factor reduces the energy flux density per point \(\xi\). In other words, the energy flux density (4) at point \(\xi\) depends not only on the acoustic pressure and the pulse duration, but also on the frequency with which the pulses are delivered. This is the hypothesis of the authors of the paper [7,8]. In real solution \(k>1\), this factor reduces the energy flux density (4), (5) with increasing frequency. The authors of work [7] blame this effect on the design of the applicator, but only for the pneumatic solution. In our study, we tried to experimentally verify the hypothesis from [7] for two different versions of the shock wave equipment: pneumatic and electromagnetic. Moreover, we put forward our hypothesis that the effect described by authors of paper [7] is caused also by the transmitter elastomer affecting the motion of the projectile (bullet)/piston and transmitter. We discuss this issue in detail in further sections. In the paper [20], it can also be found that increasing the frequency \(f\) reduces the cavitation effect of the treatment. \begin{table}
\begin{tabular}{c c c} \hline Energy Class & Lower Limit [ mJ/mm\({}^{2}\)] & Upper Limit [ mJ/mm\({}^{2}\)] \\ \hline Low & - & 0.1 \\ Medium & 0.1 & 0.3 \\ High & 0.3 & 0.6 (sometimes 0.8) \\ \hline \end{tabular}
\end{table} 
Table 1: Classifications of a shock wave–energy classes. This seems to be the result of the phenomenon shown in [7]. The design of a typical shock wave therapy generator is presented. The most common source of the EPAT shock wave in devices available on the market is the collision of two elements of the device structure. A typical apparatus (sometimes called a generator) consists of a controller and a shock wave applicator [21]. The design of the applicator seems interesting from the work point of view, so the description of the controller should only be based on the assumption that it is the component of the apparatus responsible for supplying energy (electric, potential) to the applicator. During the treatment, the physiotherapist uses the applicator by putting it on the area of the tissue with deposits or degeneration. The applicator is pressed against the patient's body in such a way that the head (also called the transmitter) is in direct contact with the skin surface.