Extended Impedance Tube Measurements of Porous Absorbers Ennes Sarradj 1 , J¨ orn H¨ ubelt 1 , Emad Elsaghir 2 , Peter Holstein 3 1 Gesellschaft f¨ ur Akustikforschung Dresden mbH, D-01099 Dresden, Germany, Email: ennes.sarradj@akustikforschung.de 2 Institut f¨ ur Akustik und Sprachkommunikation, Technische Universit¨ at Dresden, D-01602 Dresden 3 Sinus Messtechnik GmbH, D-04347 Leipzig Introduction Samples of porous absorbers are commonly characterised by their absorption coefficient α and surface impedance Z w . For measurements, standard Kundt’s tube or impedance tube method is used. Alternatively, a pair of characteristic values, e.g. charac- teristic impedance Z a and propagation constant k a may be measured by extended tube measurement techniques. To know these parameters is advantageous as they pro- vide information about the material rather than the sam- ple. This renders the prediction of the properties of sam- ples without measurements possible. Thus the design of silencers and other absorptive structures is more efficient. Measurement techniques A number of different measurement techniques are avail- able. The choice of optimal method to use for a specific sample is subject to the sample properties, e.g. high or low attenuation. In what follows, five methods are out- lined. These methods were implemented using a modular apparatus (Fig.1) and tested in a survey[1] on measure- ment techniques for characteristic values. In the two-thickness method[2], the impedance tube is used in its conventional configuration as shown below, where the normal-incidence surface impedance is mea- sured for the sample, and the same measurement is re- peated for another sample of the same material, whose thickness is the double of the first. The normal surface impedance is measured through the measurement of the transfer function between the two microphones. Due to the fact, that surface impedance under this configura- tion is related to the characteristic pair in a well-known manner, we can get the two required figures out of the two measured surface impedances the other settings of the measurement like the sample thickness, microphone locations and environmental conditions. Like the two-thickness method, the two-cavity method[3] depends on creating two different surface impedances for the sample and measuring them in the usual way, to extract then the characteristic values. How- ever, this is done in this case not through varying thick- ness, but with the same sample with varying cavity depth behind. In the method proposed by Champoux and Stin- son[4], the information needed to obtain the character- istic value pair consists of only one surface impedance measurement plus another measurement of the transfer -25 -20- -15 -10 -5 0 125 150 175 200 225 250 275 300 c in m/s a 400 600 800 1000 1200 400 600 800 1000 1200 -25 -20- -15 -10 -5 0 125 150 175 200 225 250 275 300 c in m/s a 400 600 800 1000 1200 400 600 800 1000 1200 400 600 800 1000 1200 4d 2d d 1.5d 4d with gap d Diameter of spheres Figure 2: The characteristic wave number. Upper diagram: propagation speed c  a , lower diagram: attenuation k  a . function along the sample. This is especially convenient for highly dissipative materials. The Iwase-Izume method[5] is a special version of the Champoux-Stinson method, where the depth of the cav- ity behind the sample is reduced to zero and the mi- crophones are brought directly to the sample surface for transfer function measurement. The most versatile method is the transfer-matrix method[6]. The transfer matrix coefficients of the sam- ple are determined through measuring the pressure at two points upstream and other two points downstream with the tube arbitrarily terminated. The measured transfer matrix of the absorber sample can be expressed as:  T 11 T 12 T 21 T 22  =  cos k a d A jZ A sin k A d A j Z A sin k A d A cos k a d A  . (1) Thus characteristic impedance and the wave number can be calculated from the matrix elements T . Figs. 2 and 3 contain example results for a novel ma- terial made of sintered metal hollow spheres of different diameter and packing density.