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

4.2. MATERIALS AND METHODS 55
In a series of measurements on the open tone hole, Dalmont et al. (2002) used a similar
setup to that of Keefe, but included a microphone in the passive tube termination, thereby permitting
measurement of the impedance matrix or transfer matrix. Dalmont et al. measured the
series and shunt reactances, showing that they are well-described by two theoretical studies
(Nederveen et al. 1998, Dubos et al. 1999). Dalmont et al. also measured the shunt resistance,
concluding that it may be described by a theory including viscothermal losses in the tone hole
and the radiation impedance. Since the transfer matrix was measured, results were obtained
for all frequencies in the measurement range, not just those corresponding to an impedance
extrema, although for frequencies such that sin(kL) ≈ 1, where L is the length of the measurement
tube, flow through the tone hole is essentially zero and the shunt impedance is not ‘seen’
by the apparatus.
Dalmont et al. (2002) also measured the open hole equivalent circuit at large amplitude
using a two-microphone impedance head with an extra microphone downstream of the tone
hole. This system was capable of delivering a much greater acoustic flow than the volume flow
source impedance head, allowing determination of nonlinear losses in the vicinity of the tone
hole. At high acoustic flow, resistances proportional to the velocity must be added to the series
and shunt impedances. The two-microphone method was not used for low amplitude measurements
since the authors were unable to obtain an accuracy on the length corrections lower
than 10% of the radius of the main tube.
4.2 MATERIALS AND METHODS
In the following experiments, the finger hole is placed between a pair of two-microphone impedance
heads so that the pressure and flow are measured at both sides of the hole (Figure 4.2).
From these measurements the shunt and series impedances are determined. The impedance
heads are calibrated individually using the methods of Chapter 3 and the signals applied to
each loudspeaker are adjusted to optimise the measurement of either Z s or Z a .
4.2.1 Modified impedance spectrometer
Two impedance heads with bore diameter of 15 mm are used, each equipped with two microphones;
one 10 mm from the reference plane and the other 50 mm. However, to accommodate
the finger hole, the reference plane for each head is shifted outwards from the microphones by
50 mm and the finger hole is formed in the centre of a tube section of length 100 mm.
Two nominally identical midrange loudspeakers are used as the excitation sources. Care
is taken to ensure that the loudspeakers are wired with the same polarity. It is preferable if
the distance from the reference plane to the loudspeaker is similar for each head, but this is
not essential. The voltage signal applied to one speaker is Vr and to the other V r
. The complex
factor r determines the splitting of the signal between each loudspeaker. Different loudspeaker
efficiencies may be accounted for by calibration (see §4.2.3.2).