한국음향학회지 (The Journal of the Acoustical Society of Korea)

  • 제30권7호
  • /
  • Pages.402-407
  • /
  • 2011
  • /
  • 1225-4428(pISSN)
  • /
  • 2287-3775(eISSN)
한국음향학회 (The Acoustical Society of Korea)
권호 표지
DOI QR코드

DOI QR Code

다공성 입자 매질에서 고주파 영역 음향 측정 자료와 Kramers-Krönig 관계식의 비교

Comparison of Kramers-Krönig Relation and High-Frequency Acoustic Measurements in Water-Saturated Glass Beads

  • 양해상 (서울대학교 공과대학 조선해양공학과) ;
  • 이근화 (서울대학교 공과대학 조선해양공학과) ;
  • 성우제 (서울대학교 공과대학 조선해양공학과)
  • 투고 : 2011.05.24
  • 심사 : 2011.09.27
  • 발행 : 2011.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

물리현상의 인과성에 대한 필요충분조건은 Kramers-Kr$\ddot{o}$nig (K-K) 관계식으로 표현된다. 음파에 대한 Kramers-Kr$\ddot{o}$nig 관계식은 음파의 위상속도 분산식과 감쇠계수 분산식 사이의 힐버트 변환 쌍으로 나타난다. 본 연구에서는 400 kHz-1.1 MHz의 고주파 영역에서 물이 찬 다공성 유리구슬 매질에서 측정된 p파 음속 및 감쇠계수를 Waters 등에 의해 얻어진 미분 형태의 Kramers-Kr$\ddot{o}$nig 관계식과 정량적으로 비교했다. 감쇠계수는 주파수의 거듭제곱형태를 따르며, 이때 실험값은 Kramers-Kr$\ddot{o}$nig 관계식과 비교적 정확히 일치한다.

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.

키워드

참고문헌

  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. https://doi.org/10.1364/JOSA.12.000547
  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. https://doi.org/10.1103/PhysRev.104.1760
  5. H. J. Wintle, "Kramers-Kronig analysis of polymer acoustic data," J. Appl. Phys., vol. 85, no. 1, pp. 44-48, 1999. https://doi.org/10.1063/1.369406
  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. https://doi.org/10.1121/1.2947631
  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. https://doi.org/10.1109/58.56489
  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. https://doi.org/10.1121/1.412332
  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. https://doi.org/10.1016/S0022-460X(03)00636-9
  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. https://doi.org/10.1121/1.1312364
  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. https://doi.org/10.1109/TUFFC.2003.1176526
  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. https://doi.org/10.1121/1.3153004
  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. https://doi.org/10.1121/1.396344