Lip-valve interactions with the resonant bore of a trombone

Abstract

Players of brass instruments usually play at a pitch close to one of the strong resonances of the instrument bore, but can easily play either above or below a resonance. Simple one-degree-of freedom models having aperture in phase with longitudinal lip displacement do not readily explain auto-oscillationwith realistic values of lip losses and cannot explain oscillation at frequencies below resonance. Experimental measurements of lip motion, pressures and flows show that the lips’ longitudinal motion leads the transverse: the lips move downstream closed, then open, then retract while open. Because of the forward sweeping motion, flow starts before the lips open. The sweeping motion has two important effects: first, it allows a range of phases between pressure and flow. Second, it means that the DC pressure acts on a larger area in the forward motion than during retraction. Both have consequences for oscillation energetics. A simple calculation of the PdV work done on the longitudinal component of motion, using measured quantities, indicates that it could provide a substantial fraction of the energy necessary for auto-oscillation with lossy lips. These mechanisms might have implications for other auto-oscillatory systems such as the vocal folds.