Alternative method to determine minimal load for reeds within an acoustical flow
Laurent P. Millot · The Journal of the Acoustical Society of America · 2011
To understand (free) reed(s) oscillations, a minimal acoustical load must be introduced between the excitation and the reed(s). Classically, the model for this load is either an acoustic admittance/impedance or a reflexion function. But with an existing acoustical flow as found within some experiments, the whole model should better use nonlinear acoustical flow descriptions. Considering electrofluid analogies to model local behavior of either incompressible or compressible elements, an iterative building of the acoustic load can be derived from which, for each studied load, a pure recursive linear filtering of the excitation can be found. With a time-independent excitation, the acoustic load can create instabilities or not according to the filter poles. Using this method one can find again the minimal load to explain oscillations of either single blown-closed or blown-open reed but also the minimal description of the vocal tract needed for chromatical playing on diatonic harmonica. It is also possible to easily derive the numerical approximation of the acoustic load and reed(s) equations using a single numerical scheme, if a highly sufficient sampling frequency is chosen (maybe greater than 44.1 or 48 kHz), to perform numerical simulations of the studied acoustical problem.