  In unbounded media, the acoustic attenuation as function of frequency is
related to the frequency-dependent sound velocity (dispersion) via
Kramers-Kronig dispersion relations. These relations are fundamentally
important for better understanding of the nature of attenuation and dispersion
and as a tool in physical acoustics measurements, where they can be used for
control purposes. However, physical acoustic measurements are frequently
carried out not in unbounded media, but in acoustic waveguides, e.g. inside
liquid-filled pipes. Surface acoustic waves are also often used for physical
acoustics measurements. In the present work, the applicability of
Kramers-Kronig relations to guided and surface waves is investigated using the
approach based on the theory of functions of complex variables. It is
demonstrated that Kramers-Kronig relations have limited applicability to guided
and surface waves. In particular, they are not applicable to waves propagating
in waveguides characterised by the possibility of wave energy leakage from the
waveguides into the surrounding medium. For waveguides without leakages, e.g.
those formed by rigid walls, Kramers-Kronig relations remain valid for both
ideal and viscous liquids. In the former case, Kramers-Kronig relations express
the exponential decay of non-propagating (evanescent) higher-order acoustic
modes below the cut-off frequencies via the dispersion of the same modes above
the cut-off frequencies. Examples of numerical calculations of wave dispersion
and attenuation using Kramers-Kronig relations, where applicable, are presented
for unbounded media and for waveguides formed by rigid walls.
