Kramers–Kronig relationship between ultrasonic attenuation and phase velocity

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Abstract
Kramers–Kronig relations linking the attenuation and dispersion are presented for a linear acousticsystem. These expressions are used as a starting point to derive approximate, nearly local expressions relating the ultrasonic attenuation at a specific frequency to the local frequency derivative of the phase velocity (i.e., dispersion). The validity of these approximate relationships is demonstrated in several acoustic systems exhibiting substantially different physical properties.