## 2 Characteristics of the Shock Wave and Its Sources
The amplitude of the pulse is expressed in the measured quantity--the voltage at the hydrophone terminals, which corresponds to the instantaneous acoustic intensity. The first non-negative part of the wave, called the positive phase, stands for a sharp pressure increase in the medium. This phase typically lasts 1-100 \(\upmu\)s, and the generated pressure can reach 80 MPa [1; 13; 14; 15]. Figure 1: Example of a shock wave pulse. The wavefront, in the form of a monotonic pressure increase in the positive phase is responsible for the shock effect [14] consisting in alternating compression and stretching of the material, for example, in water [18]:  
\[t_{r}=\frac{5}{\Delta p}\ \ \ \ \ [\text{ns}] \tag{1}\]  
where:  
\(t_{r}\)--duration of the rising edge of the positive phase,  
\(\Delta p\)--pressure amplitude change. It then breaks deposits and stones into smaller pieces--generally speaking, hard objects in the tissue. In the case of stones, under specific conditions, we can observe the Hopkins effect, which is the spallation of broken deposits as a result of reflection in the counter-phase of the shock wave from the boundaries of the stone and tissue centers [1,2]. The broken material is absorbed and then excreted by the body. As already mentioned, the positive phase of the shock wave consists in a sharp increase in pressure. Due to the inertial nature of physical phenomena, the return to the state of pressure equilibrium in the tissue is associated with the occurrence of a temporary negative pressure (the so-called negative phase--a non-positive wave fragment in Figure 1). It is worth noting that the same inertia causes the return to the state of equilibrium associated with the occurrence of damped shock wave resonance at a given point in the medium, i.e., alternating progressively smaller positive and negative phases. It relates both to the inertia of the particle vibration itself and also to the formation of further shock waves on a micro scale resulting from an explosion of deposits and hardening in the tissue [1]. In addition, it will also be related to another phenomenon called cavitation--described as a momentary phase change in the medium related to the occurrence of sudden negative pressure. A typical example of cavitation is air bubbles flowing around a rotating ship propeller. \[\frac{dp}{dT}=\frac{L}{T\Delta V} \tag{2}\]  
where:  
_dp/dT_--pressure derivative along the phase transition curve,  
\(L\)--enthalpy of phase change,  
\(T\)--tissue water temperature,  
\(\Delta V\)--volume change. Tissue pressure drop by Clausius-Clapeyron is given by Equation (2), causing a rapid decrease in the boiling point of water in the tissue, which results in the formation of gas bubbles [2,13] (unidirectional diffusion [14] according to Fick's Laws [17]). Immediately afterward, the bubbles, while collapsing, implode and generate successive shock waves, which, as in the example with the ship, are the source of the sound and allow you to track the object by listening to the water tank with a hydrophone. Referring to the example at the beginning of the section, a cavitation bubble rupture can be compared to an air balloon rupture. Successive shock waves generate further local cavitation phenomena, which, in turn, are the source of the shock waves. This is an example of a typical chain reaction that is quenched in each subsequent step. Another pro-healing effect is associated with the collapse of the follicles, i.e., microjets (funnel-shaped microstructure) supporting the rupture of degenerative areas [14]. Experts estimated the speed of this stream at 130-170 m/s [14]. To sum up, all the above-mentioned phenomena, i.e., the shock effect, cavitation generating penetrating gas bubbles, and microjets, are pro-therapeutic in nature. They can be used in the non-invasive crushing of kidney stones (lithotripsy), treatment of tennis elbow, heel spurs, and elimination of cellulite (aesthetic medicine).