Sound dispersion and attenuation in the thickness direction of paper materials

Abstract

A through-transmission, dry-contact ultrasonic technique aimed at investigating sound propagation in the thickness direction of paper materials is presented. The method uses piezoelectric ceramic transducers immersed in fluid-filled rubber wheels. Thickness and longitudinal velocity are determined from time domain measurements for several commercial paper specimens between 40 and 1750 μm. Dispersion and attenuation are reported at frequencies up to 1.5 MHz. Dispersion is less than 10% between 0.25 and 1.25 MHz. Amplitude calculations are used to evaluate the attenuation coefficient versus the frequency. Using a nearly local form of the Kramers–Kronig relationships, the attenuation coefficient is also obtained from the phase information. By comparing the amplitude- and phase-determined attenuation coefficients, an apparent reflection coefficient is predicted. It is shown that the Kramers–Kronig relationships can be applied to papers thicker than 200 μm under dry coupling conditions. The attenuation coefficient is inversely related to the elastic stiffness for homogeneous specimens. A linear relationship is observed between the attenuation loss and the thickness. The apparent reflection coefficient correlates to the apparent surface roughness of paper.