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Extended Impedance Tube Measurements of Porous Absorbers

1

Ennes Sarradj1 , J¨rn H¨belt1 , Emad Elsaghir2 , Peter Holstein3 o u

Gesellschaft f¨r Akustikforschung Dresden mbH, D-01099 Dresden, Germany, Email: [email protected] u

2

Institut f¨r Akustik und Sprachkommunikation, Technische Universit¨t Dresden, D-01602 Dresden u a

3

Sinus Messtechnik GmbH, D-04347 Leipzig

Introduction

ca in m/s

300 275 250 225 200 175 150 125 400 0 -5 -10 600 800 1000 spheres of 1200

Samples of porous absorbers are commonly characterised by their absorption coefficient 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. characteristic impedance Z a and propagation constant k a may be measured by extended tube measurement techniques. To know these parameters is advantageous as they provide information about the material rather than the sample. This renders the prediction of the properties of samples without measurements possible. Thus the design of silencers and other absorptive structures is more efficient.

d Diameter 4d 2d d 1.5d 4d with gap

Measurement techniques

A number of different measurement techniques are available. 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 outlined. These methods were implemented using a modular apparatus (Fig.1) and tested in a survey[1] on measurement 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 measured for the sample, and the same measurement is repeated 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 configuration 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. However, this is done in this case not through varying thickness, but with the same sample with varying cavity depth behind. In the method proposed by Champoux and Stinson[4], the information needed to obtain the characteristic value pair consists of only one surface impedance measurement plus another measurement of the transfer

-15 -20-25 400 600 800 1000 1200

Figure 2: The characteristic wave number. Upper diagram: propagation speed ca , lower diagram: attenuation ka .

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 cavity behind the sample is reduced to zero and the microphones 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 sample 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 21 T 12 T 22 =

j ZA

cos k a dA sin k A dA

jZ A sin k A dA cos k a dA

.

(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 material made of sintered metal hollow spheres of different diameter and packing density.

Amplifier

Impedance-Tube-Based Measurement System for Acoustical Properties of Porous Materials

PCMCIA

Harmonie

ICP Microphones Back Volume

The four-channel DSP Harmonie provides the output test signals and records and processes the response of the system with the help of an extremely flexible user-tailored programming capability.

Sample Holder

Upstream Waveguide

Rigid Termination

Loudspeaker Adapter Downstream Waveguide It is used with the upstream waveguide to measure transfer characteristics along the sample Loudspeaker with Hole Rigid Termination with Hole This part is used with a microphone fitted in the Hole to terminate the tube, when pressure measurement is intended directly at the back surface of the sample. Anechoic Termination When this part is filled with highly porous absorber, it acts as a quasi matched termination.

Back Volume with Hole

Loudspeaker Adapter with Hole

Microphone-Carrying Rod It carries a microphone, which traces the pressure along the axis of the tube (SWR method), or if pressure is to be measured directly at the front surface of the sample.

Figure 1: Modular apparatus for the implementation of several measurement techniques

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References

[1] E. Elsaghir: Messverfahren zur Bestimmung von Absorberparametern. Master's thesis, Institut f¨r u Akustik und Sprachkommunikation, TU Dresden, 2003 [2] Pyett, J.: Acoustic impedance of a porous layer at oblique incidence. Acustica 3, (1953), 375­382

d Diameter of spheres 4d 2d d 1.5d 4d with gap

[3] Yaniv, S.: Impedance Tube Measurement of Propagation Constant and Characteristic Impedance of Porous Acoustical Materials. J. Acoust. Soc. Am. 54 (5), (1973), 1138-1142 [4] Champoux, Y. and Stinson, M.: Measurement of the Characteristic Impedance and Propagation Constant of Materials Having High Flow Resistivity, J. Acoust. Soc. Am. 90 (4), (1991), 2182-2191 [5] Iwase, T. and Kawabata, R.: Measurements of basic acoustical properties of the porous pavement and their application to the estimation of road traffic noise reduction. J. Acoust. Soc. Jpn., 20 (1), (1999),63­74 [6] B. Song and J. S. Bolton: A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials. J. Acoust. Soc. Am. 107 (3), (2000), 1131­1152

3 2 1 0 -1 -2 -3

Figure 3: The characteristic impedance Z A . Upper diagram: Magnitude of Z A , lower diagram: Phase of Z A .

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