RESUMO
This paper investigates how two-port network theory as a means for system identification can be applied to the analysis of brass instruments. A special focus is placed on the energy conversion efficiency as this is limited by inner damping, which receives much attention by expert players and makers of brasses. Theory suggests that a reconstruction of the 2 × 2 matrix representing the network requires input impedance and transfer function for two different boundary conditions. Besides the normal case of free sound radiation, instruments are also analyzed with the bell closed by a spherical cap. For this purpose, a customized 3D-printed spherical cap was fabricated and attached to the bell. Four measured spectra and the passivity condition over-determine the set of system equations. It is shown how to take advantage of this freedom when analyzing wind instruments. Measurements and simulations of a trumpet and a trombone are presented and compared.
RESUMO
It has recently been proposed that the effects of structural vibrations on the radiated sound of brass wind instruments may be attributable to axial modes of vibration with mode shapes that contain no radial nodes [Kausel, Chatziioannou, Moore, Gorman, and Rokni, J. Acoust. Soc. Am. 137, 3149-3162 (2015)]. Results of experiments are reported that support this theory. Mechanical measurements of a trumpet bell demonstrate that these axial modes do exist in brass wind instruments. The quality factor of the mechanical resonances can be on the order of 10 or less, making them broad enough to encompass the frequency range of previously reported effects attributed to bell vibrations. Measurements of the input impedance show that damping bell vibrations can result in impedance changes of up to 5%, in agreement with theory. Measurements of the acoustic transfer function demonstrate that the axial vibrations couple to the internal sound field as proposed, resulting in changes in the transfer function of approximately 1 dB. In agreement with theory, a change in the sign of the effect is observed at the frequency of the structural resonance.
RESUMO
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.
RESUMO
The results of an experimental and theoretical investigation of the influence of wall vibrations on the sound of brass wind instruments are presented. Measurements of the transmission function and input impedance of a trumpet, with the bell both heavily damped and freely vibrating, are shown to be consistent with a theory that assumes that the internal pressure causes an oscillation of the diameter of the pipe enclosing the air column. These effects are shown to be most significant in sections where there are flaring walls, which explains why damping these vibrations in cylindrical pipes normally produces no measurable effects.
