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

34 CHAPTER 3. MEASURING ACOUSTIC IMPEDANCE
Table 3.1: Several of the more common impedance heads, with conditions for singularities, selected references and notes. In the expressions for singularities,
k is the wavenumber and n = 1,2,3,.... The reference plane is indicated by a vertical dashed line.
Impedance Head Singularities Refs. Notes
(a) volume flow source kd = (2n − 1) π 2
Singh & Schary (1978), Benade & Ibisi
(1987), Bruneau (1987), Wolfe et al.
d
• computationally simple
• requires calibration of the source
(2001a)
• prone to errors at high |Z |
(b) pulse reflectometer f -range limited by
pulse width
Fredberg et al. (1980), Watson &
Bowsher (1988)
• uses same microphone for incident and
reflected wave; calibration unnecessary
• accuracy limited by length of measurement
duct
(c) two microphones
kd = (n − 1)π Seybert & Ross (1977), Chung & Blaser
(1980a,b,c), Bodén & Åbom (1986),
Åbom & Bodén (1988), Gibiat & Laloë
d
(1990), van Walstijn et al. (2005)
• fewer simplifying assumptions required
• computationally intensive
(d) volume flow source with
upstream microphone
d
kd = (2n − 1) π 2
Backus (1974, 1976), Caussé et al.
(1984)
• signal from upstream microphone
proportional to flow (for an attenuator with
high impedance compared to the unknown
load)
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