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

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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
5.3. RESULTS AND DISCUSSION 85 10 8 10 7 m s (Pa 10 6 |Z| − 3 ) 10 5 model experiment 10 4 0 1 2 3 4 f (kHz) Figure 5.17: Impedance spectra (experiment and model) for the modern flute with all holes closed and the holes ignored in the model. 10 8 10 7 m s (Pa 10 6 |Z| − 3 ) 10 5 model experiment 10 4 0 1 2 3 4 f (kHz) Figure 5.18: Impedance spectra (experiment and model) for the modern flute with all holes closed and without any keypad correction.
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Flute acoustics: measurement, model
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To Renée iii
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vi I am grateful to my parents, Ros
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x 4.4 Conclusions and further direc
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2 CHAPTER 1. INTRODUCTION and the p
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4 CHAPTER 1. INTRODUCTION Figure 1.
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12 CHAPTER 2. THEORY AND LITERATURE
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k = ω c and pressure given by p(x,
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142 APPENDIX A. IMPEDANCE SPECTRA C
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338 APPENDIX C. QUANTIFYING MUSIC s
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340 REFERENCES Botros, A., Smith, J
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342 REFERENCES Kob, M. & Neuschaefe
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