• The Journal of the Acoustical Society of Korea
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• v.30 no.7
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• pp.402-407
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• 2011

The necessary and sufficient condition for causality of a physical system can be expressed as Kramers-Kr$\ddot{o}$nig (K-K) relation. K-K relation for acoustic wave is a Hilbert transforms pair between dispersion equations of phase speed and attenuation. In this study, we quantitatively compare the acoustic measurements in water-saturated glass beads for the frequency ranges from 400 kHz to 1.1 MHz with the predictions of differential form of K-K relation obtained by Waters et al. For media with attenuation obeying an arbitrary frequency power law, acoustic measurements show good agreements with the predictions of Kramers-Kr$\ddot{o}$nig relation.