Evaluation of the acoustical stiffness of saxophone reeds under playing conditions by using the reactive power approach

Abstract

The dynamics of a saxophone reed has been analyzed by means of the simplest model—one pure spring—acceptable for frequencies below the resonance frequency of the reed. As proposed in the context of bowed string dynamics [J. Acoust. Soc. Am. 90, 754–763 (1991)], a reactive power is defined for the air-column of a saxophone and its reed. When the instrument sustains a harmonic tone, a balance between those two reactive powers can be established, as a generalization onto a multimodal system of the usual condition sin(φ)=0 that a simple oscillator fulfills when it vibrates at its resonance frequency. The stiffness of the reed can be derived from that condition. Experiments were carried out on a saxophone played by a professional musician. The reed stiffness under playing conditions is determined after separate measurements of the input impedance (TMTC method) and of the internal pressure spectrum. Results are comparable with compliance values measured on isolated reeds by other authors.