Lévy Stable Distribution and 0,2 Power Law Dependence of Acoustic Absorption on Frequency in Various Lossy Media

Absorption of acoustic wave propagation in a large variety of lossy media is characterized by an empirical power law function of frequency, α₀|ω|^y. It has long been noted that the exponent y ranges from 0 to 2 for diverse media. Recently, the present author J. Acoust. Soc. Am. 115 (2004) 1424
developed a fractional Laplacian wave equation to accurately model the power law dissipation, which can be further reduced to the fractional Laplacian diffusion equation. The latter is known underlying the Lévy stable distribution theory. Consequently, the parameters y is found to be the Lévy stability index, which is known to be bounded within 0