Head Joint, Embouchure Hole and Filtering Effects on the Input Impedance of Flutes

A study of Z(f), the input impedance of the Boehm flute, measured from 200 Hz to 12.5 kHz shows the expected set of strong resonances in the frequency range that corresponds to fundamental frequencies of the playing regime. These frequencies are below the expected cut-off frequency (due to an array of open tone holes) for propagation along the bore of the flute. Above this frequency, in a range that affects the harmonics rather than the fundamental of played notes, the inertive reactance of the tone holes increases with frequency until the standing wave propagates along the tone hole lattice with little attenuation. Harmonic resonances are again evident, but now correspond to resonances of the whole length of the instrument. However the resonances associated with the bore are strongly attenuated over an intermediate frequency range. This appears to be a consequence of a Helmholtz resonator formed by the air in the embouchure hole and the sealed end of the head joint. Experiments with different head joints confirm this mechanism. The envelope of Z(f) shows a broad maximum near 10 kHz that we attribute to the resonance of the embouchure riser tube.