Experimental verification of the Kramers-Kronig relationship for acoustic waves

A spectral technique for effectively and accurately measuring acoustic attenuation over a wide frequency range is reported. The spectral technique for phase measurement developed by W. Sachse and Y.H. Pao (1978) was used to determine the acoustic dispersion. For acoustic waves, a very simple and useful Kramers-Kronig relationship was previously derived by M. O'Donnell, E.T. Jaynes, and J.G. Miller (1981). The attenuation was calculated, using this relationship, from the measured dispersion and then compared with the attenuation that was measured independently. Dispersion was deduced from the measured attenuation and compared with the measured dispersion. The results of two highly attenuative specimens are presented. The agreement between the calculated attenuation and measured attenuation is excellent. The deduced dispersion also agrees well with the measured one. This agreement verifies the simple Kramers-Kronig relationship used. It further shows the accuracy of the spectral techniques for attenuation and dispersion measurements over a wide frequency range.