Trombone lip mechanics with inertive and compliant loads (“lipping up and down”)

Trombonists normally play at a frequency slightly above a bore resonance. However, they can “lip up and down” to frequencies further above the resonance (more compliant load) and below (inertive load). This was studied by determining the pressures, flows, and acoustic impedance upstream and downstream and by analyzing high-speed video of the lips. The range of lipping up and down is roughly symmetrical about the peak in bore impedance rather than about the normal playing frequency. The acoustic flow into the instrument bore has two components: the flow through the lip aperture and the sweeping flow caused by the moving lips. Variations in the phases of each of these two components with respect to the mouthpiece pressure allow playing regimes loaded by bore impedances varying from compliant to inertive. In a simple model, this sweeping motion also allows the pressure difference across the lips to do work on the lips around a cycle. Its magnitude is typically about 20 times smaller than the work input to the instrument but of the same order as the maximum kinetic energy of the lips. In some cases, this sweeping work may, therefore, contribute most or all of the energy required for auto-oscillation.