Flute acoustics: measurement, modelling and design - School of ...

84 CHAPTER 5. IMPEDANCE SPECTRA OF THE FLUTE AND CLARINET
10 8
10 7
|Z| (Pa s m −3 )
10 6
10 5
10 4
model
experiment
0 1 2 3 4
f (kHz)
Figure 5.16: Impedance spectra (experiment and model) for a closed classical headjoint after
adjustment of parameters.
tone holes—these were totally ignored in the model. The model fit in Figure 5.17 is close to the
experimental data but in the model the impedance extrema are slightly higher in frequency.
This is expected since a closed side hole acts mainly as a compliance (Nederveen 1998) and
nearly always lowers the frequency.
Figure 5.18 shows the same experimental data with a model including the closed tone holes.
The model uses the physical dimensions of each hole with the impedance corrections given in
§2.2.10. Each hole is terminated by an infinite impedance. The extrema predicted by this model
are slightly lower in frequency than measured. For this reason, the correction
t keypad =−0.05b (5.4)
was applied to the hole length (here, as in §2.2.10, b refers to the hole radius). The resulting
model fit is shown in Figure 5.19. This correction is physically reasonable, since the keypad
protrudes a small distance into the hole chimney and reduces the compliance of the closed
hole. The impedance spectrum was also measured for the flute playing C4 with all keypad
perforations plugged (not shown here). There was negligible difference between the spectra,
indicating that the extra volume created by the keypad perforations and the impedance of the
player’s fingers are negligible in this situation.
5.3.4.2 One hole open
To test and refine the flute impedance model for a flute fingering with open holes, the fingerings
C♯4 and A4 (diffuse) were tested on the modern flute with C foot. These fingerings each