Demonstration of nonlinear mode coupling in woodwind-like air columns: Recollections from the laboratory of A. H. Benade

Abstract

Self sustained oscillations in woodwinds are generated by the player's blowing pressure, through the interaction of the standing wave in the air column, the dynamic motion of the reed and the air flow through the reed. In properly designed instruments, the oscillation begins at a threshold blowing pressure near the frequency of an air column resonance. With increased blowing pressure, the amplitude grows and the flow nonlinearity generates harmonics of the playing frequency. The nonlinearity couples the steady state components of the tone. The coupling dictates behaviors that cannot be explained by a linear model. When A. H. Benade came to understand this in the early 1960s, he developed a “tacet horn” whose unplayable behavior could only be explained by the nonlinear theory [Benade and Gans, Ann. N.Y. Acad. Sci. 155, 247–263 (1968)]. Throughout his life, Benade used other pathological air columns for research and pedagogy. This paper will demonstrate two of Benade’s concepts with air columns that are simple to build. One is a clarinet-like tube that can play softly near threshold, but cannot be played louder. The other is a conical tube that plays only at high amplitude.