Chapter 6: Impedance measurements

Acoustic impedance measurements
Phase [DEG]
30
20
10
0
Phase sample corr [deg]
30
0
-30
-10
-60
-20
-90
-30
100 1k
Frequency [Hz]
100 1k
Frequency [Hz]
Fig. 6.14 (left): Corrected free field phase response of a pu probe. At the flipping’
frequencies the response is obtained by interpolation. Fig. 6.15 (right): The corrected
phase response of the acoustic sample in the tube.
absorbtion
1,0
absorbtion
0,5
0,0
100 1k
Frequency [Hz]
Fig. 6.16: Absorption coefficient measured in the Kundt’s tube.
The ‘free field’ phase response (the phase response measured in a tube
but corrected for the tube’s behaviour, Fig. 6.14) is used to correct the
phase response of the absorbing sample in the tube (Fig. 6.14, grey line):
see Fig. 6.15.
Now the modulus (Fig. 6.12) and the phase response ( Fig. 6.15) of the
impedance due to the acoustic sample are known, the absorption coefficient
can be calculated with Eq. (6.7), see Fig. 6.16.
Relation between impedance and reflection coefficient
As shown above, the reflection coefficient is given by the ratio of the
outward travelling pressure wave and the incoming travelling pressure wave
(Eq. (6.2) and Eq. (6.3)).
( ω)
p ( x ) = p e ⎫⎪ p R e
→ = =
p ( x ) = p R e ⎪⎭
ikx
−ikx
in 0 p
out
( x ) 0 −2ikx
R
ikx
( ω)
e
−ikx
⎬
out 0 ( ω)
p
in( x ) p0
e
(6.16)
The inward and sound waves cannot be measured directly with a
pressure microphone or a Microflown.
6-17