Acoustical behavior of brass player’s lips

Abstract

The controversial problem of whether a brass player's lip movements are best modeled as outward striking or as upward striking is approached by measuring the phase difference between mouthpiece pressure and lip displacement. In analogy with the phase of the input impedance to a resonant system, the negative/positive value of this phase difference suggests an outward-striking/upward-striking oscillation. On the basis of this speculation, the experimental results revealed the following: (1) Large lip-driven pipes support both outward-striking and upward-striking oscillations because of the lip's high flexibility in the absence of a mouthpiece; (2) mouthpiece-nonresonant tube systems almost support the outward-striking oscillation over a wide frequency range; (3) mouthpiece-resonant tube systems totally support the outward-striking oscillation; (4) the French horn and trumpet exhibit the outward-striking oscillation for the lowest mode and the upward-striking oscillation for higher modes. The oscillation transition in brass instruments, which corresponds well to the change of mouthpiece pressure waveform from a low-pitch, nonsinusoidal one to a higher-pitch, more sinusoidal one, depends mainly on the nonlinear acoustic impedance of the lip opening. If its magnitude is negligible, the cavity coupling between the mouthpiece cup and player's mouth yields a capacitive input impedance that favors the outward-striking oscillation; if its magnitude is significant, the cavity decoupling is likely to yield an inertive input impedance that favors the upward-striking oscillation. Since both the time-varying Bernoulli pressure at the lip opening and the area receiving this pressure are generally apt to increase as the blowing pressure increases, the upward-striking oscillation tends to dominate higher mode tones in brass instruments.