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Trumpet sound simulation is carried out with a two-dimensional lip vibration model, where the lips execute both swinging and stretching motions. This model allows lips to operate on both the lower and higher frequency sides of the air-column resonance frequencies. Oscillations generated by the total sound production system are on both the lower and higher frequency sides in the first through third resonance modes, while in the fourth and higher modes they are realized only on the lower side. From each resonance mode, an oscillation having the least frequency deviation against a change in lip eigenfrequency and also having sufficient amplitude is selected as the optimum oscillation of the resonance mode. It is found that these oscillations in the lower modes have positive phase differences between lip vibration and mouthpiece pressure, whereas those in the higher modes have negative ones. This result closely matches the transition of lip vibration states from the one modeled by the outward-striking valve at the second mode (i.e., the lowest mode among those used musically) to that modeled by the laterally striking valve at the higher modes, which is observed in the simultaneous measurement of mouthpiece pressure and lip vibration.
Adachi et al. (Thu,) studied this question.