Axial vibrations of brass wind instrument bells and their acoustical influence: Theory and simulations

Abstract

Previous work has demonstrated that structural vibrations of brass wind instruments can audibly affect the radiated sound. Furthermore, these broadband effects are not explainable by assuming perfect coincidence of the frequency of elliptical structural modes with air column resonances. In this work a mechanism is proposed that has the potential to explain the broadband influences of structural vibrations on acoustical characteristics such as input impedance, transfer function, and radiated sound. The proposed mechanism involves the coupling of axial bell vibrations to the internal air column. The acoustical effects of such axial bell vibrations have been studied by extending an existing transmission line model to include the effects of a parasitic flow into vibrating walls, as well as distributed sound pressure sources due to periodic volume fluctuations in a duct with oscillating boundaries. The magnitude of these influences in typical trumpet bells, as well as in a complete instrument with an unbraced loop, has been studied theoretically. The model results in predictions of input impedance and acoustical transfer function differences that are approximately 1 dB for straight instruments and significantly higher when coiled tubes are involved or when very thin brass is used.

Axial vibrations of brass wind instrument bells and their acoustical influence: Experiments

“…16 has recently been extended by Kausel et al, who demonstrated theoretically how the whole-body motion of brass wind instruments can couple to the internal sound field and how this coupling can explain many of the observed effects on the radiated sound of the instrument under normal playing conditions. 19 Their results of computer modeling of a simplified trumpet indicate that this coupling is broad-band and frequency dependent, in agreement with previous experimental results. Furthermore, the results predict that whole-body motion can either increase or decrease the amplitude of the acoustic transfer function (ATF), which is defined as the ratio of the acoustic pressure in the open air in front of the bell to that in the mouthpiece.…”

“…In what follows, we present experimental evidence of the interaction between the vibrating walls and the internal air column of a trumpet bell similar to that predicted in Ref. 19. In Sec.…”

“…These results are also compared to the results of simulations presented in Ref. 19. Finally, the crossover frequency determined from the ATF is shown to occur at the same frequency as the mechanical resonance identified in the MTF.…”

“…These results are also compared to the results of simulations using the model presented in Ref. 19. In Sec.…”

La acústica de los instrumentos musicales de viento - metal

“…[7][8][9] Del mismo modo, casi todos los ejecutantes de estos instrumentos creen firmemente que los efectos de las vibraciones del instrumento tienen un efecto significativo en el sonido. Esto ha demostrado ser cierto en el caso de las vibraciones de la campana 10 y se ha propuesto una teoría para explicar el efecto, 11,12 pero no está claro que las vibraciones de otras partes del instrumento afecten al sonido.…”