Sound, physics boundary conditions

All methods described above can be categorized as automated case-by-case simulations based on accidents. There are two more aspects which are of importance for a sound system evaluation during the pre-crash phase. Many processes involved are deterministic, e.g., the participants dynamics, the technical functions implemented, as well as many physical boundary conditions. However, some of the key processes do have a stochastic nature for example, the driver action and reaction as well as some characteristics, e.g., of the sensors modeled. Due to the sensitivity of the results to those processes, stochastic elements are an important feature of any representative evaluation (see also Sect. 3.4). 

Coherent reflections at the top and bottom boundaries of the plate give way for a set of standing acoustic waves between the two main surfaces of the plate. Due to the piezoelectric nature of quartz two sets of resonance frequencies exist for each mode, depending on the electrical boundary conditions. The first set corresponds to a plate with open-circuit boundary conditions. From the physical point of view charges will be collected on the electrodes building up a potential difference and hence an electrical field from the electrical point of view the electrodes are unconnected. This resonance is termed anti-resonance in the piezoelectric literature and parallel resonance in electronics literature. The second set of resonance frequencies corresponds to a plate with short-circuit boundary conditions. The electrodes are connected and a potential difference cannot be built up. The respective names are resonance in piezoelectric and series resonance in electronics Hterature. The differences arise from piezoelectric stiffening accompanied by differences in the sound velocity. The anti-resonance (parallel) frequencies of each of the three acoustic modes are completely decoupled giving ... 

Joining two tubes creates a boundary condition at the junction, and it is this junction which determines how the sound propagates as a whole. In considering behaviour at a junction, we can use an important principle of physics which states that pressure and volume velocity caimot change instantaneously anywhere. So despite the sudden change in cross sectional area, the volume velocity and pressure caimot abruptly change, and it follows from this that at the point of the junction the pressure and volume velocity must be equal. Hence... 

---