On the indirect measurement of airflow resistivity of thin specimens in mid-frequencies via measured transfer matrix (T12)

Recent experiments demonstrated that airflow resistivity (AFR) of fibrous porous materials can be calculated indirectly via impedance and transmission loss tubes in the mid-frequency region [Pandey and Jena (2025). Meas. Sci. Technol. 36, 035901]. In the present work, a method for estimating AFR is devised using the second element, T12, of the four-pole parameters or the transfer matrix (T), of the given porous material, as measured via a transmission loss tube. The theoretical background is discussed first, followed by the finite element simulation [conducted according to ASTM (2019a) E2611-19 standard] on fourteen materials, sourced from literature, with AFR ranging from ∼ 2 to 99 kPa·s/m2. It is observed that these results depend significantly on the sample thickness, and by keeping the thickness in the range of 10-15 mm, the AFR can be estimated in a broadband mid-frequency region with errors of ≤ 2.6%. At last, experiments are conducted on five materials, three (fibrous materials, high AFR) having samples of three different thicknesses and the other two (low AFR) having thicknesses of 10 mm and 15 mm. The results are presented to authenticate the observations made from simulations, followed by the uncertainty analyses to determine the reliability.