Chapter 6: Impedance measurements

Acoustic impedance measurements
frequencies f u and f p the response is measured not accurately. Therefore the
response around these frequencies is estimated by interpolation.
The amplitude response of the uncorrected impedance (black line Fig.
6.10) can be converted in the free field response (Fig. 6.11) by:
Z
ff
f
sin( π )
= fu
Ztube,
rigid
π f
(6.15)
cos( )
2 f
p
The normalised impedance of the sample is given by the ratio of the
measured response of the sample in the tube (as shown in Fig. 6.10, grey
line) and the free field response (as shown in Fig. 6.11). The result is given
in Fig. 6.12.
Normalised impedance [-]
100
10
1
Z sample lin
phase [DEG]
150
100
50
0
-50
Ph sample
ph r=1
-100
0,1
100 1k
Frequency [Hz]
-150
100 1k
Frequency [Hz]
Fig. 6.12 (left): Normalized impedance at the position of the pu probe an absorbing
sample at the end. Fig. 6.13 (right): Phase response in the tube. Black line: rigid
termination, grey line: with an acoustic sample at the end.
The phase response of the pu probe in the standing wave tube is shown
in Fig. 6.13. The black line shows the phase response of the pu probe with a
rigid termination, the grey line shows the response when the absorbing
sample is mounted at the end of the tube.
First the phase response of the pu probe is determined as if the probe is
used in the free field. The free field phase response is obtained by
correcting the measured phase response in the impedance tube with the
phase of the known standing wave in the tube. In the rigidly closed tube the
phase of the sound field is ±90 degrees so in order to get the free field
response, 90 degrees is added for frequencies up to f p . This is the frequency
of the pressure minimum (at 1494Hz) and this is also the frequency where
the tube response flips from -90degrees to 90 degrees. In the frequency
range from f p to f u (the velocity minimum at 3263Hz), 90 degrees is
subtracted. At frequencies higher than f u , 90 degrees is added again. The
phase response is not smooth around the frequencies f p and f u . Therefore,
at these frequencies the phase is kept constant to get a better estimation.
The result is shown in Fig. 6.14.
6-16