Acustica

Characteristic dimensions and prediction at high frequencies of the surface impedance of porous layers
Denis Lafarge, Jean F. Allard, and Bruno Brouard
Laboratoired91coustique, C.N.R.S. URA No. 1101, Facult• desSciences Mans, B.P. 535, Ave. Olivier du
Messiaen, F-72017 Le Mans C•dex, France

ChristineVerhaegen and Walter Lauriks
LaboratoriumvoorAkoestiek, KatholiekeUniversiteit Leuven,Celestijnenlaan D, B-3001, Heverlee, 200 Belgium

(Received 15 May 1992; revised19 January 1993; accepted27 January 1993) The surfaceacoustic impedance a glasswool and a reticulatedfoam is measured a free field of in up to 20 000 Hz. The characteristic dimensions and A' can be calculatedfor the glasswool, A and the surfaceimpedancecan be predictedwith no adjustableparameters.The motion of the frame is not taken into account.The agreement betweenmeasurement and predictionis good. For the foam, the characteristicdimensions cannot be calculated,because the geometryof the frame is not simple. A correct choiceof A and A' allows a preciseprediction of the surface impedancefor a large range of frequencies and different thicknesses. PACS numbers: 43.20.Gp, 43.20.Jr, 43.20.Rz, 43.55.Ev

INTRODUCTION

In animportant paper, Johnson aL1gave simple et a expression the effective for densityp of a fluid saturating a porousmedium, which simultaneously takes into account the inertial and the viscousforces,and presentsa correct asymptoticbehavior at high frequencies. indicated by As
Johnson,the exact expression the effectivedensity canfor not be calculatedfor the case of porous materials with a frame having a complicatedgeometry,but the asymptotic high-frequency behaviorcan be predictedif the tortuosity

Both Eqs. (1) and (2) are identical when the square velocitiesare removed. For the caseof identical cylindrical pores, v(M) is a constant that can be removed from Eq. ( 1) and the two characteristic dimensions equal. If the are poresdo not have a constantcrosssection,the dimension

A