JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Comparison of Kramers-Krönig Relation and High-Frequency Acoustic Measurements in Water-Saturated Glass Beads
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Comparison of Kramers-Krönig Relation and High-Frequency Acoustic Measurements in Water-Saturated Glass Beads
Yang, Hae-Sang; Lee, Keun-Hwa; Seong, Woo-Jae;
  PDF(new window)
 Abstract
The necessary and sufficient condition for causality of a physical system can be expressed as Kramers-Krnig (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-Krnig relation.
 Keywords
Kramers-Krnig relation;porous medium;p-wave sound speed and attenuation;water-saturated glass beads;
 Language
Korean
 Cited by
 References
1.
H. M. Nussenzveig, Causality and Dispersion Relations, Academic Press, New York, 1972.

2.
R. de. L. Krönig, "On the theory of dispersion of x-rays," J. Opt. Soc. Amer. Rev. Sci. Instrum., vol. 12, pp. 547-556, 1926. crossref(new window)

3.
H. A. Kramers, "Diffusion of light by atoms," Atti Congr. Int. Fis. Como., vol. 2, pp. 547, 1927.

4.
J. S. Toll, "Causality and the dispersion relation: Logical foundations," Phys. Rev., vol. 104, pp. 1760-1770, 1956. crossref(new window)

5.
H. J. Wintle, "Kramers-Kronig analysis of polymer acoustic data," J. Appl. Phys., vol. 85, no. 1, pp. 44-48, 1999. crossref(new window)

6.
F. J. Alvarez and R. Kuc, "Dispersion relation for air via Kramers-Kronig analysis," J. Acoust. Soc. Am., vol. 124, no. 2, pp. EL57-EL61, 2008. crossref(new window)

7.
C. C. Lee, M. Lahham, and B. G. Martin, "Experimental verification of the Kramers-Kroing relationship for acoustic waves," IEEE Trans. Ultrason. Ferroelect. Freq. Contr., vol. 37, no. 4, pp. 286-294, 1990. crossref(new window)

8.
T. L. Szabo, "Causal theories and data for acoustic attenuation obeying a frequency power law," J. Acoust. Soc. Am., vol. 97, no. 1, pp. 14-24, 1995. crossref(new window)

9.
Z. E. A. Fellah, S. Berger, W. Lauriks, and C. Depollier, "Verification of Kramers-Kronig relationship in porous materials having a rigid frame," J. Sound Vib. vol. 270, no. 4-5, pp. 865-885, 2004. crossref(new window)

10.
M. O'Donnell, E. T. Jaynes, and J. G. Miller, "General relationships between ultrasonic attenuation and dispersion," J. Acoust. Soc. Am., vol. 63, no. 3, pp. 696-701, 1981.

11.
J. Mobley, K. R. Waters, M. S. Hughes, C. S. Hall, J. N. Marsh, G. H. Brandenburger, and J. G. Miller, "Kramers-Kronig relations applied to finite bandwidth data from suspensions of encapsulated microbubbles," J. Acoust. Soc. Am., vol. 108, no. 5, pp. 2091-2106, 2000. crossref(new window)

12.
K. R. Waters, M. S. Hughes, J. Mobley, and J. G. Miller, "Differential forms of the Kramers-Krönig dispersion relations," IEEE Trans. Ultrason. Ferroelect. Freq. Contr., vol. 50, no. 1, pp. 68-76, 2003. crossref(new window)

13.
K. Lee, E. Park and W. Seong, "High frequency measurements of sound speed and attenuation in water-saturated glassbeads of varying size," J. Acoust. Soc. Am., vol. 126, no. 1, pp. EL28-EL33, 2009. crossref(new window)

14.
E. Pfaffelhuber, "Generalized impulse response and causality," IEEE Trans. Circuit Theory, vol. CT-18, no. 2, pp. 218-223, 1971.

15.
R. D. Costley and A. Bedford, "An experimental study of acoustic waves in saturated glass beads," J. Acoust. Soc. Am., vol. 83, no. 6, pp. 2165-2174, 1988. crossref(new window)