## 3 Experiments and Results  
### Measurement of Energy Surface Density Using a Piezoelectric Vibrometer  
Performing device tests for therapeutic procedures outside the living organism requires using a phantom equivalent to the operated tissue. In such a situation, care should be taken to ensure that the phantom or experimental environment resembles the target center, i.e., the tissue of the body, with its properties. In the context of the shock wave, two solutions are possible. One is to prepare a phantom that imitates tissue (in terms of hardness, etc.). For example, a water cushion, a pork carcass [24], or magnetic levitation (the authors' attempts in the past) can be used. The second refers to performing the entire experiment (immersing the transmitter and the sensor) in a liquid with similar parameters as the tissue (e.g., water) [7]. This section presents the method of measuring the shock wave using the first approach, i.e., a phantom and a piezoelectric vibrometer. The performed experiments by immersing the transmitter and hydrophone in a water tank presents the next section. As presented in the previous section, the generation of the shock wave is related to the movement of the transmitter pressed against the operated tissue. Therefore, it is possible to measure the oscillations (vibrations) which the tissue (here, the phantom) is set in after the projectile or piston has hit the transmitter. The SparkFun SEN-09196 piezoelectric vibrometer (model LDT0-028K) was used for this purpose. The authors in the paper [22] used a laser vibrometer to measure the vibrations of the transmitter, but the issue of its pressure against the phantom was omitted (only the free movement of the transmitter was measured). Moreover, the authors of the paper [10] applied yet another approach. They used a load cell to measure the force transformed into shock wave energy. The entire construction of the experimental test bench is presented in Figure 6. The sensor is a flexible piezo-polymer PVDF foil, which generates a voltage at its terminals depending on the strength of vibration and bending. This voltage was further processed in the analog-digital system by reading the voltage values (the GwInstek GDS-1054B oscilloscope was used). An important element of the test bench was the phantom (water pillow) to which the transmitter of the applicator (mounted in a specially prepared stand) was pressed by a vibrometer (by a laboratory jack stand). The use of a lab jack allowed us to achieve a real-like pressure of the applicator to the operated tissue. In paper [7], the authors used a spring for this purpose. We also used a gel to support the coupling of the centers and the propagation of the shock wave. As a phantom, we used a water pillow (with distilled water), which allowed the shock wave, after penetrating a thin layer of the pillow membrane (LDPE polyethylene), to propagate in the water medium as if it were in real tissue. The experiment includes setting the operating parameters of the generator, i.e., power and frequency, and recording 100 pulses of the shock wave. For each impulse of the shock wave (vibration), a Newton-Cotes quadrature of the zero order of the phase of the positive shock wave was determined. We integrate only the fragment of the signal waveform in which the wave impulse occurs. Moreover, we averaged the quadrature (trimmed mean). It is worth mentioning that we retained the value of the voltage generated at the terminals of the vibrometer, not converting it to other units because we aimed to compare the results for different configurations rather than to determine the value of the selected measure more precisely. The voltage signal of the vibrometer corresponds (after rescaling based on the sensor characteristics) to the instantaneous acoustic intensity (3), which is an integrant function for the energy flux density in formula (4). In other words, the integration over time of the voltage signal of the vibrometer corresponds to integration over time of the acoustic intensity.