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Absorption Mechanisms and Physical Constraints

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Waves with Power-Law Attenuation

Abstract

The spring–damper models for viscosity and relaxation described in Chap. 2 can be justified in processes taking place at length scales which may be much smaller than the wavelength, often at the molecular level. This is especially so in the acoustics case. In Sect. 2.6.3 specific examples of processes were given due to \(H_2O\), \(MgSO_4\), and \(B(OH)_3\) for seawater as well as \(O_2\) and \(N_2\) for air. This chapter begins with a more detailed account of these processes starting with the simplest monatomic and polyatomic gases, simple and associated liquids, and finally chemical solutions.

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Notes

  1. 1.

    A stricter criterion was applied in Buckingham (2018) making the result more in agreement with what is developed here.

  2. 2.

    http://www.claymath.org/millennium-problems/navier-stokes-equation.

References

  • B. Angelsen, Ultrasonic Imaging: Waves, Signals, and Signal Processing, vol. 1–2 (Emantec AS, Trondheim, 2000)

    Google Scholar 

  • P. Ball, Water: water-an enduring mystery. Nature 452(7185), 291–292 (2008)

    Google Scholar 

  • A.B. Bhatia, Ultrasonic Absorption: An Introduction to the Theory of Sound Absorption and Dispersion in Gases, Liquids, and Solids (Courier Dover Publications, New York, 1967)

    Google Scholar 

  • D.T. Blackstock, Fundamentals of Physical Acoustics (Wiley, New York, 2000)

    Google Scholar 

  • M.J. Buckingham, Causality, Stokes’ wave equation, and acoustic pulse propagation in a viscous fluid. Phys. Rev. E 72(2), 026610 (2005)

    Google Scholar 

  • M.J. Buckingham, On the transient solutions of three acoustic wave equations: van Wijngaarden’s equation, Stokes’ equation and the time-dependent diffusion equation. J. Acoust. Soc. Am. 124, 1909 (2008)

    Google Scholar 

  • M.J. Buckingham, Wave-speed dispersion associated with an attenuation obeying a frequency power law. J. Acoust. Soc. Am. 138(5), 2871–2884 (2015)

    Google Scholar 

  • M.J. Buckingham, The dispersion formula and the green’s function associated with an attenuation obeying a frequency power law. J. Acoust. Soc. Am. 144(2), 755–765 (2018)

    Google Scholar 

  • K. Cheng, T. Fujii, Heat in history Isaac Newton and heat transfer. Heat Transf. Eng. 19(4), 9–21 (1998)

    Google Scholar 

  • L.B. Evans, H.E. Bass, L.C. Sutherland, Atmospheric absorption of sound: theoretical predictions. J. Acoust. Soc. Am. 51(5B), 1565–1575 (1972)

    Google Scholar 

  • C.L. Fefferman, Existence and smoothness of the Navier-Stokes equation, The Millennium Prize Problems (Clay Mathematics Institute, Cambridge, 2006), pp. 57–67

    Google Scholar 

  • L.S. García-Colín, R.M. Velasco, F.J. Uribe, Beyond the Navier-Stokes equations: Burnett hydrodynamics. Phys. Rep. 465(4), 149–189 (2008)

    Google Scholar 

  • M.E. Gurtin, A.C. Pipkin, A general theory of heat conduction with finite wave speeds. Arch. Ration. Mech. Anal. 31(2), 113–126 (1968)

    Google Scholar 

  • L. Hall, The origin of ultrasonic absorption in water. Phys. Rev. 73(7), 775 (1948)

    Google Scholar 

  • A. Hanyga, Wave propagation in linear viscoelastic media with completely monotonic relaxation moduli. Wave Motion 50(5), 909–928 (2013)

    Google Scholar 

  • A. Hanyga, Dispersion and attenuation for an acoustic wave equation consistent with viscoelasticity. J. Comput. Acoust. 22(03), 1450006-1–22 (2014)

    Google Scholar 

  • S. Holm, M.B. Holm, Restrictions on wave equations for passive media. J. Acoust. Soc. Am. 142(4) (2017)

    Google Scholar 

  • S. Holm, S.P. Näsholm, Comparison of fractional wave equations for power law attenuation in ultrasound and elastography. Ultrasound. Med. Biol. 40(4), 695–703 (2014)

    Google Scholar 

  • S. Jennings, The mean free path in air. J. Aerosol. Sci. 19(2), 159–166 (1988)

    Google Scholar 

  • L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders, Fundamentals of Acoustics, 4th edn. (Wiley, New York, 1999)

    Google Scholar 

  • R. Ludwig, Water: from clusters to the bulk. Angew. Chem. Int. Ed. 40(10), 1808–1827 (2001)

    Google Scholar 

  • R.M. Lynden-Bell, S.C. Morris, J.D. Barrow, J.L. Finney, C. Harper, Water and Life: The Unique Properties of H2O (CRC Press, New York, 2010)

    Google Scholar 

  • J.J. Markham, R.T. Beyer, R.B. Lindsay, Absorption of sound in fluids. Rev. Mod. Phys. 23(4), 353–411 (1951)

    Google Scholar 

  • M. Matsumoto, S. Saito, I. Ohmine, Molecular dynamics simulation of the ice nucleation and growth process leading to water freezing. Nature 416(6879), 409–413 (2002)

    Google Scholar 

  • J. Mobley, Simplified expressions of the subtracted Kramers-Kronig relations using the expanded forms applied to ultrasonic power-law systems. J. Acoust. Soc. Am. 127(1), 166–173 (2010)

    Google Scholar 

  • M. O’Donnell, E. Jaynes, J. Miller, Kramers-Kronig relationship between ultrasonic attenuation and phase velocity. J. Acoust. Soc. Am. 69, 696–701 (1981)

    Google Scholar 

  • S. Santucci, D. Fioretto, L. Comez, A. Gessini, C. Masciovecchio, Is there any fast sound in water? Phys. Rev. Lett. 97(22), 225701 (2006)

    Google Scholar 

  • M. Seredyńska, A. Hanyga, Relaxation, dispersion, attenuation, and finite propagation speed in viscoelastic media. J. Math. Phys. 51(9), 092901-1–16 (2010)

    Google Scholar 

  • N.W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction (Springer, Berlin, 1989). Reprinted in 2012

    Google Scholar 

  • G. Verma, Ultrasonic absorption due to chemical relaxation in electrolytes. Rev. Mod. Phys. 31(4), 1052 (1959)

    Google Scholar 

  • K.R. Waters, J. Mobley, J.G. Miller, Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 822–823 (2005)

    Google Scholar 

  • R.L. Weaver, Y.H. Pao, Dispersion relations for linear wave propagation in homogeneous and inhomogeneous media. J. Math. Phys 22, 1909–1918 (1981)

    Google Scholar 

  • R.H. Winterton, Heat in history. Heat Transf. Eng. 22(5), 3–11 (2001)

    Google Scholar 

  • E. Yeager, F. Fisher, J. Miceli, R. Bressel, Origin of the low-frequency sound absorption in sea water. J. Acoust. Soc. Am. 53(6), 1705–1707 (1973)

    Google Scholar 

  • C. Zener, Elasticity and Anelasticity of Metals (University of Chicago Press, Chicago, 1948)

    Google Scholar 

  • X. Zhao, R.J. McGough, Time-domain comparisons of power law attenuation in causal and noncausal time-fractional wave equations. J. Acoust. Soc. Am. 139(5), 3021–3031 (2016)

    Google Scholar 

Download references

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Holm, S. (2019). Absorption Mechanisms and Physical Constraints. In: Waves with Power-Law Attenuation. Springer, Cham. https://doi.org/10.1007/978-3-030-14927-7_4

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