Incorporating the wind-chest reservoir and a foot model to the organ pipe time domain simulation
Résumé
It is not new to pursue a closed formulation of the organ pipe operation that leads to a feasible solution in time or frequency. Research contributions in the 1950'-60' brought up again the question of the nature of the aero-acoustic sources in such instruments well after the Rayleigh-Helmholtz dispute. Said contributions marked and accelerated a progress line: from the simple resonator with passive radiating ends, to the mouth impedance, its coupling with the volume upstream behind the formation point of the jet, plus its receptivity, instability, and convection. If one neglects all other less prominent contributions to sound, all those finally lead to a dipole-like source in the labium at the mouth of the pipe (inwards / outwards). Most of these mechanisms are common with flue-like instruments. A further contribution is presented here in order to obtain greater realism and a more accurate description: the incorporation of the conical cavity, or foot, whose response is coupled with the window. The model is compared with measurements of the pressure in the reservoir (the wind-chest in the real organ), in the foot, inside the resonator, and the radiated field in the vicinity of the mouth. A model is proposed regarding the influence of the volume of the foot on the pressure rise time in the resonator, the efficiency and quality of the first modes of oscillation in the transient state. Lastly, for the sake of computational affordability of a real- time realisation, accuracy of the linearised model is discussed.
Domaines
Acoustique [physics.class-ph]
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