Sound production in air-jet driven wind instruments
Douglas H. Keefe, Ioana Valeriu · The Journal of the Acoustical Society of America · 1990
Models of sound production in air jet-driven wind instruments are constructed in which the air-jet flow need not be small relative to the flow through the mouth of the organ flue pipe (or embouchure hole of the flute). This case is important for initial transients in wind instruments. The transverse flute differs from the organ in that the air jet interacts with two resonators rather than one, and this interaction is modeled using mass and momentum conservation to the mixing region of the air jet with the acoustical field. The linear system difference is most important. Separate reflection functions, defined in terms of pressure, are needed for the main body of the flute and the flute head joint volume. The dynamical system is expressed in terms of three first-order differential equations involving the air-jet flow, and the displacement and volume flow through the mouth. Transverse instabilities propagating along the jet are controlled by the current and time-delayed mouth displacement, the latter reflecting the wave speed of the instability across the mouth [N.H. Fletcher, J. Acoust. Soc. Am. 60, 926–936 (1976)], but our calculations are limited insofar as the frequency dependencies of the delay time and amplification factor of the transverse instability are neglected. Time domain simulations are well suited for investigating the relative importance of nonlinear flow and momentum injection mechanisms, and preliminary results will be discussed.