Impedance phase-dependent correction factor for a tonehole model

Abstract

The upper and lower end corrections of an open tonehole in a woodwind instrument are often accommodated by adding them to the physical thickness of the wall to create an effective thickness used in calculating the impedance of the tonehole. A rough estimate of the correction often used is 1.5 time the tonehole radius (1.5b), while other more rigorous treatments yield values in this vicinity. These values are usually independent of frequency or are constrained to a range of geometric tonehole and bore dimensions. The data from this study showed a strong and significant frequency dependency that produced a large range of correction values between about 0.5b and 1.5b. This variation correlated with the phase of the impedance of the highest open tonehole, and generally increased with increasing sounding frequency. This paper will discuss the conditions under which the measurements were made and how the correction factors were obtained, and will propose how the observed frequency dependence can be incorporated into the correction factor through the phases of the impedances of the open toneholes.