On the applicability of Kramers-Kronig relations for ultrasonic attenuation obeying a frequency power law
In the recent literature concern has been raised regarding the validity of Kramers-Kronig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers-Kronig dispersion relations for application to these types of media are available. The developed dispersion relations are compared with measurements on several liquids, and agreement is found to better than 1 m/s over the experimentally available bandwidth. A discussion regarding the validity of these dispersion relations, in particular how the dispersion relations relate to the so-called Paley-Wiener conditions, forms the conclusion.
Waters
KR
Department of Physics, Washington University, St. Louis, Missouri 63130-4899, USA.
Hughes
MS
Mobley
J
Brandenburger
GH
Miller
JG