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

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88 CHAPTER 5. IMPEDANCE SPECTRA OF THE FLUTE AND CLARINET 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 5.22: Impedance spectra (experiment and model) for the fingering C♯4 on the modern flute using (2.30) to model the extra impedance caused by the overhanging keypad. available for radiation and hence lead to a greater than expected length correction. For these reasons, an empirical correction may be required. Figure 5.22 shows the model fit for C♯4 and Figure 5.23 shows the model fit for the fingering A4 (diffuse) with measured key dimensions (h, the height of the disk above the hole perimeter was taken to be that at the hole axis). 5.3.4.3 Two holes open In the previous section, the model was used to model the impedance of fingerings with one open hole. The model was then tested on the fingering D4, in which two consecutive holes are open. Figure 5.24 shows the prediction of the model compared with experiment using the corrections applied in the previous section. The model overestimates the height and depth of impedance extrema, particularly in the region 1.5–2.5 kHz. For this reason, the resistance R open hole = 0.4Z 0 (kb) 2 (5.5) was added to the radiation impedance of the open hole (k here is the wavenumber and b is the radius of the hole). Dalmont et al. (2001) do not address the the effect of an overhanging keypad on the real part of the radiation impedance; the increase seen here (albeit indirectly) is physically quite plausible. Inspection of Figure 5.25 reveals that over the frequency range 1.5–2.5 kHz the model locates the impedance extrema at frequencies slightly higher than measured. In this frequency range (encompassing the cut off frequency) the radiation impedance of open holes has the
5.3. RESULTS AND DISCUSSION 89 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 5.23: Impedance spectra (experiment and model) for the fingering A4 (diffuse) on the modern flute using (2.30 and 2.32) to model the extra impedance caused by the overhanging keypad.
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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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6 CHAPTER 1. INTRODUCTION 1.5 ACOUS
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10 CHAPTER 1. INTRODUCTION
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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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32 CHAPTER 3. MEASURING ACOUSTIC IM
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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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