For both trials, the higher frequencies were generally harder to excite than the low frequencies. In the first trial, resonant frequencies were produced that did not correspond to resonance modes, for flip values in the middle of two impedance peaks. In contrast, no resonant modes were excited above the third in either trial. Based on the trials conducted, it is not possible to determine whether the model can function in the higher range, since both the flip and ξequily values were chosen in relatively large increments. It is possible that the higher resonance modes need more precision in the choice of one or both of these parameters to be excited. This would correlate with trumpet players' experience that it is easier to excite oscillations between resonance modes, or "lip bends" in the low range than in the high range. Since Adachi and Sato found that the resonance modes were excited using frequencies below the impedance peaks in the low range, and above in the high range, it makes sense that directly using the impedance peak values for flip would not excite the resonance modes, and that frequencies slightly above or below the modes should be investigated. In addition to testing flip values that are closer together across the full tested range, values could be tested slightly above and below the resonance peaks to try to excite them. It is also possible that different blowing pressure values than those used by Adachi and Sato could be used to excite the modes, or that changing the lip parameters that were assumed by Adachi and Sato could produce different results. More investigation is needed, first in the choice of flip and ξequily, and then for other parameters, before conclusions can be drawn about the behaviour of the resonance modes in the high range.
The method chosen for selecting values for ξequily is both inefficient and only considers one of the selection criteria given by Adachi and Sato. Since the values are chosen by looking at a plot of the pressure produced and choosing the one with the largest oscillation amplitude, the condition that the lips must only come into contact for much shorter than an oscillation period is not considered or checked. A method that considers this condition as well may yield more reliable results. Additionally, looking at the plot for each value of ξequily means that each trial takes significantly longer than it would if the process were automated. Therefore, a method where these criteria were checked automatically for each value of ξequily tested would be far more efficient, and would likely yield results more accurate to Adachi and Sato (1996). This more efficient would allow for smaller increments to be used to test ξequily without taking much more time. An even more efficient and effective method would be to find a way to explicitly derive the optimal value of ξequily, which Adachi and Sato state depends only flip.
Some model features from Adachi and Sato (1996) are also left out. When the lips are closed, the quality factor of the lips should change from 3.0 to 0.5, and an extra restoring force should be added along the y-axis with stiffness 3k. Incorporating these changes may make the results for accurate to those found by Adachi and Sato.
This project provides a preliminary investigation into Adachi and Sato's 1996 model, but conclusions cannot be drawn from the results of the mode excitation trials without further investigating the selection of ξequily, using flip values in smaller increments, and incorporating the elements from Adachi and Sato (1996) that were left out from this investigation. After this further work and investigation, a comparison plot of excitation frequencies and impedance peaks can be made for these results and compared with those in Figure 4 from Adachi and Sato (1996). The relative contributions of the two models could also be investigated, and compared with Adachi and Sato's results.