An impedance tube submerged in a liquid for the low-frequency transmission-loss measurement of a porous material

Abstract According to the standard ASTM E2611 an impedance tube can be used to measure the sound transmission and reflection losses in an absorption material. However, application in a liquid medium in the low-frequency range presents difficulties with respect to the size of the structure and the waveguide-related distortion of the plane-wave propagation. In this paper a four-microphone impedance tube for use in liquids in the low-frequency range, complying with the transfer-matrix method for transmission-loss measurements, is presented. The impedance tube is validated on the basis of research on an underwater, two-microphone impedance tube. It is demonstrated that in the low-frequency range the loudspeaker couples well into the plane-wave propagation. Furthermore, existing methods for measuring the group velocity and the complex wavenumber, applicable to the impedance tube, were investigated and compared to the new methods developed in this article. The results showed the best fits for the cross-correlation and the new approach of amplitude matching, respectively, for the cases of the velocity and the wavenumber measurements. Thus, the validated impedance tube was used for acoustic measurements of metal-foam samples. Problem-specific equations for calculating the dissipation coefficients of cavity-backed samples were derived from the transfer matrix and the scattering matrix. Stable results in agreement with the expected low absorption were obtained.