On the applicability of Kramers–Krönig relations for ultrasonic attenuation obeying a frequency power law

In the recent literature concern has been raised regarding the validity of Kramers–Krönig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers–Krönig 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.