Acoustic waves in discrete media, similarities at meso and nano scales

Abstract

In this paper the similarities between the acoustic behavior of a discrete medium of random arrangement of solid spheres, at mesoscopic scales, and thermal vibrations of lattice ions in crystalline solid, at nano scales, are investigated. Results for the ultrasonic waves in random media show that such effects as cutoff frequency, wave dispersion, energy distribution in vibration modes, wave attenuation by scattering and absorption, observed in discrete media, have close resemblance to the similar phenomena observed at atomic scales, such as phonons or lattice thermal vibration of atoms in the crystalline solids. For example, the cutoff frequency in lattice vibration is related to the interatomic spacing, similarly, the cutoff frequency at mesoscopic scales depends on grain separation or grain size. These similarities are also observed in wave scattering and attenuation and their dependence on wave number, kR (k=2π/λ and R is particle size). In this paper experimental measurements with data analysis on cutoff frequency, wave attenuation, and wave dispersion related to the above mentioned similarities will be presented, and the extension of these findings to the behavior of acoustic waves in other discrete media will be discussed.