Kramers–Kronig analysis of polymer acoustic data

Wintle, H. J.

doi:10.1063/1.369406

Cited by 16 publications

(4 citation statements)

References 10 publications

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“…Since their introduction in the 1920s in relation to the absorption of light scattered by atoms, they have been used in many different fields of Physics to build causally consistent models. Ginzberg is credited with being the first one to propose a particular form of the K-K relations for acoustic applications, giving rise to numerous works that have used evolved versions of these expressions to relate attenuation and phase velocity in the measurements of soft tissues, 1 polymers, 2 suspensions, 3,4 and cancellous bone, 5 to give some examples. Traditionally, the application of these integral relations has involved two problems.…”

Section: Introductionmentioning

confidence: 99%

Dispersion relation for air via Kramers-Kronig analysis

Álvarez¹,

Kuc²

2008

The Journal of the Acoustical Society of America

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A general expression for the dispersion of acoustic waves in air is obtained by combining the attenuation coefficient given by the ISO:9613-1 standard and the twice-subtracted Kramers-Kronig relation. Good agreement is found with published data of sound velocity at different frequencies and relative humidities. The resulting expression is used to investigate changes in local dispersion with temperature and humidity.

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Section: Introductionmentioning

confidence: 99%

Dispersion relation for air via Kramers-Kronig analysis

Álvarez¹,

Kuc²

2008

The Journal of the Acoustical Society of America

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“…While the choice of c is arbitrary, and the quantities mЈ, mЉ must be scaled appropriately, 4 we will choose c to be the high frequency limit, and then the components of the moduli are directly related to susceptibilities Ј, Љ which are entirely analogous to the dielectric case:…”

Section: A Velocity Formulaementioning

confidence: 99%

Power law absorption in polymers and other systems

Wintle

2000

The Journal of the Acoustical Society of America

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The theoretical treatment of acoustic absorption which goes as a power of the frequency is quite subtle. In this paper, it is shown that some of the difficulties can be resolved by using a wide distribution of relaxation times which is cut off at a short time limit 1 Ͼ0, and a finite long time limit 2 Ͻϱ, without altering the general form of the acoustic response. This formalism is used to show that quadratic, linear, and fractional losses can be consistent with the Kramers-Kronig ͑KK͒ causal relations. The linear loss in polymers is associated with a weak velocity dispersion, so the group velocity and the phase velocity are quite close. The implications for space charge measurements in insulating polymers are discussed. Using the Helmholtz-Kirchhoff tube absorption as an example, it is also shown that the local approximation for the KK relations is unsatisfactory.

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“…Refs. [4][5][6][7][8][9][10][11][12][13]. Note that Kramers-Kronig relations are the sequence of causality and linearity of the medium 14 .…”

Section: Introductionmentioning

confidence: 99%