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

CHAPTER 3. MEASURING ACOUSTIC IMPEDANCE 50
(a)
10 6
10 4
10 8
(b)
10 6
|Z| (Pa s m -3 )
10 4
10 8
(c)
10 6
10 4
10 8
(d)
10 6
|(Z meas - Z theo ) / Z theo |
10 8 (e)
10 4
10 0
10 -2
10 -4
0 1 2 3 4
Frequency (kHz)
Figure 3.5: The input impedance for a closed 15 mm pipe, 200 mm long. In (a) and (b) the signals
from microphones 2 and 3 were multiplied by 1.2 and 0.8 respectively to deliberately introduce
errors. The impedance was measured before calibration (a) and after calibrating using
one known load (b). In (c) the impedance is given for matched microphones before (grey, solid
line) and after (black, dotted line) calibration with two known loads, and in (d) the calibrated
measurement from (c) (black, dotted line) is compared with the theoretical impedance for an
ideal tube (grey, solid line). The fractional difference between this theory and the measurement
is shown in (e).