Building Acoustics

Sound absorbers 163

where d = x 2 - x 1. This is the basic equation when using this two-microphone method to
determine reflection factor, impedance and intensity.
Implementing this method to determine the reflection factor and impedance implies
that the probe microphone in the classical method is substituted by two pressure
microphones separated by a given distance d (see Figure 5.6). Here the distance from the
microphone no. 1 (closest to the loudspeaker) to the surface of the specimen is denoted l.
Feeding the loudspeaker with a broadband signal; the total pressure transfer function H 12
between the positions 1 and 2 is determined. Again assuming that there are no energy
losses in the tube we may transform the reflection factor, according to Equation (5.11), to
the position of the surface of the specimen. We then get

0

0

0

j

12 j2

j

12

(0, )

kd

kl

kd

He

Rf e

eH

− −

=⋅

−

. (5.12)

l

To analyser

Broadband

signal

d

Loudspeaker Specimen

Figure 5.6 Impedance measurement set-up using a two-microphone method.

Knowing the refection factor we may easily calculate the input impedance of the
specimen by inserting Equation (5.12) into Equation (5.3). After some algebra we get

(^) g0 012 0 0
012
sin( ) sin ( )
(0, ) j.
cos ( ) cos( 0 )
H kl k l d
Zf c
kl d H kl
ρ

−−⎡⎣ ⎤⎦

=

⎡⎤⎣⎦−−

(5.13)

We shall present some measurement results below using this method (see e.g. Figures
5.15 and 5.26).
Lastly, it should be mentioned that determining the basic transfer function H 12
several types of broadband signals are in use; stochastic noise, MLS signals and swept
sine (SS) signals. There is also the possibility of using just one microphone moved
between positions assuming that the signal is reproducible. No calibration to account for
the mismatch between microphones is then necessary.

5.3.3 Reverberation room method (ISO 354)

Product data specifying the absorption capability of materials are normally determined
by measurements in a diffuse field using the so-called reverberation room method. The
specifications applying to this method are found in the international standard ISO 354.
We have already discussed the method in connection with the diffuse field theory for
rooms (see section 4.5.1.2). We shall therefore just briefly repeat the basic principle. It is
based on the Sabine formula for the reverberation time in a room: