Experiments on the single woodwind tone hole

Abstract

Impedance parameters associated with the lumped T circuit representing the tone hole in the woodwind musical instrument transmission-line model are measured for two types of tone holes. One type has a diameter large relative to the height of the tone-hole chimney, as on the saxophone. The other type has a chimney height nearly equal to the hole diameter, as on the clarinet. The imaginary parts of the series and shunt impedances, measured under small signal conditions, agree with predicted values, and the closed-hole series impedance data agree with earlier data of Nederveen and van Wulfften Palthe [Acustica 13, 65–70 (1963)]. A semi-empirical expression is deduced, by use of measurements of Bouasse [Tuyaux et Resonators (Librairie Delagiare, Paris, 1929), p. 239], Benade and Murday [J. Acoust. Soc. Am. 41, 1609 (1967)], and the theory of Keefe [J. Acoust. Soc. Am. 72, 676 (1982)], for the open-hole effective length te of a tone hole with a pad suspended above it. This expression correctly predicts the values of te for the two types of tone holes measured as well as for the flute tone-hole data obtained by Coltman [J. Acoust. Soc. Am. 65, 499–506 (1979)]. The open-hole shunt resistance, which includes radiation loss from the open-hole, viscous shearing loss in the bulk of the air, and wall loss at the sharp corners of the hole and within the hole chimney, is measured. The ratio of the radiation resistance to the total shunt resistance for a single hold varies systematically with frequency. This ratio is low at low frequencies due to large losses at the corners and edges, is a maximum near 750 Hz for sax-type holes and decreases again at higher frequencies due to increased shearing losses.