The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
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Comparison of Kramers-Krönig Relation and High-Frequency Acoustic Measurements in Water-Saturated Glass Beads

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

  • 양해상 (서울대학교 공과대학 조선해양공학과) ;
  • 이근화 (서울대학교 공과대학 조선해양공학과) ;
  • 성우제 (서울대학교 공과대학 조선해양공학과)
  • Received : 2011.05.24
  • Accepted : 2011.09.27
  • Published : 2011.10.31
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Abstract

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.

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.

Keywords

References

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