# Propagation Characteristics of Acoustic Wave in Non-Isothermal Earth’s Atmospheres

### Abstract

Acoustic waves are those waves which travel with the speed of sound through a medium. H. Lamb (1909, 1910) had derived a cutoff frequency for stratified and isothermal medium for the propagation of acoustic waves. In order to find the cutoff frequency many methods were introduced after Lamb's work. In this paper, we have chosen the turning point frequency method following Musielak et.al(2006) Routh et. al.(2014) to determine cutoff frequencies for acoustic waves propagating in non-isothermal medium which can be applied to various atmospheres like solar atmosphere, stellar atmosphere, earth's atmosphere etc. Here, we have analytically derived the cutoff frequency and have analyzed and compared with the Lamb's cut-off frequency for earth's troposphere.

### References

[2] T. M. Brown and R.L. Gilliland, “Asteroseismology,” Ann. Rev. Astron. Astrophys. 32, pp. 37, 1994.

[3] T. M. Brown, B.M. Mihalas and J. Rhodes, Jr., in Physics of the Sun, Ed. Peter A. Sturrock, vol. 1, pp. 177, 1987.

[4] L. M. B. C. Campos, “On waves in gases. Part I: Acoustics of jets, turbulence and ducts,” Rev. Mod. Phys., vol. 58, pp. 117, 1986.

[5] L. M. B. C. Campos, “On waves in gases. Part II: Interaction of sound with magnetic and internal modes,” Rev. Mod. Phys., 59, pp. 363, 1987.

[6] M. Cavcar, The International Standard Model, home.anadolu.edu.tr/ mcavcar/common/ISAweb.pdf, retrieved on 28/03/2017.

[7] D. Deming et al., “A search for p-mode oscillations in Jupiter:Serendipitous observations of non-acoustic thermal wave structure,” Astrophys. J., vol. 343, pp. 456, 1989.

[8] R. Hammer, Z. E. Musielak, and S. Routh, “The origin of cutoff frequencies for torsional tube waves propagating in the solar atmosphere,” AN, vol. 331, pp. 593, 2010.

[9] C. J. Hansen, D.E. Winget and S.D. Kawaler, “Evolution of the pulsation properties of hot pre-white dwarf stars,” Astrophys. J., vol. 297, pp. 544, 1985.

[10] N. Kobayashi and N. Nishida, “Continuous excitation of planetary free oscillations by atmospheric disturbances,” Nature, vol. 395, no. 6700, pp.357, 1998.

[11] H. Lamb, Hydrodynamics. Dover, New York, 1932.

[12] H. Lamb, “On the theory of waves propagated vertically in the atmosphere,” Proc. Lond. Math. Soc., vo. 7, pp. 122, 1909.

[13] H. Lamb, “The dynamical theory of sound,” Proc. R. Soc. London, A, vol. 34, pp. 551, 1910.

[14] U. Lee, Astrophys. J., vol. 405, pp. 359, 1993.

[15] D. W. Moore, and E.A. Spiegel, “The Generation and Propagation of Waves in a Compressible Atmosphere,” Astrophys. J., vol. 139, pp. 48, 1964.

[16] P. M. Morse and H. Feshbach, Methods of Theoretical Physics. McGraw Hill, New York, 1953.

[17] P. M. Morse and K. U. Ingard, Theoretical Acoustics. Princeton Uni. Press, Princeton, 1986.

[18] Z. E. Musielak, D. E. Musielak and H. Mobashi, “Method to determine cutoff frequencies for acoustic waves propagating in nonisothermal media,” Phys. Rev. E, vol. 73, pp. 036612-1, 2006.

[19] Z. E. Musielak, S. Routh, and R. Hammer, “Cutoff-free propagation of torsional alfven waves along thin magnetic flux tubes,” ApJ, vol. 660, 2007.

[20] Z. E. Musielak, D.E. Winget and M. Montgomery, “Atmospheric Oscillations in White Dwarfs: A New Indicator of Chromospheric Activity,” Astrophys. J., vol. 630, pp. 506, 2005.

[21] E. M. Salomons, Computational Atmospheric Acoustics. Kluwer Acad. Publ., Dordrecht, 2002.

[22] F. Schmitz and B. Fleck, “On wave equations and cut-off frequencies of plane atmospheres,” Astron. Astrophys., vol. 337, pp. 487, 1998.

[23] N. Suda, K. Nawa and Y. Fukao, “Earth’s background free oscillations,” Science, vol. 279, no.5359, 1998, pp.2089-2091.

[24] P. B. Subrahmanyam, R. I. Sujith and T.C. Lieuwen, “Propagation of Sound in Inhomogeneous Media: Exact, Transient Solutions in Curvilinear Geometries,” J. Vibration and Acoustics, vol. 125, 133, 2003.

[25] D. Summers, “Gravity Modified Sound Waves in a Conducting Stratified Atmosphere,” Quart. J. Mech. Appl. Math., 29, pp. 117, 1976.

[26] J. H. Thomas, “Magneto-Atmospheric Waves,” Ann. Rev. Fluid Mech., vol. 15, pp. 321, 1983.

[27] D. R. Raichel, The Science and Applications of Acoustics. Springer Science and Business Media, New York, 2006.

[28] T. D. Rossing and N.H. Fletcher, Principles of Vibrations and Sound. Springer-Verlag, New York, 2004.

[29] D. O. Revelle, “Annals of the New York Academy of Sciences,” The United Nations Conference on Near-Earth Objects, Vol. 822, pp. 284–302, May, 1997.

[30] S. Routh, Propagation and generation of waves in solar atmosphere, Dissertation, University of Texas at Arlington, 2009.

[31] S. Routh, Z. E. Musielak and R. Hammer, “Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes,” Sol. Phys., vol. 246, pp. 133, 2007.

[32] S. Routh and Z. E. Musielak, “Propagation of acoustic waves in the non isothermal solar atmosphere,” Astronomische Nachrichten, vol. 335, no. 10, pp. 1043-1048, 2014.

[33] S. Routh, Z. E. Musielak and R. Hammer, “Temperature Gradients in the Solar Atmosphere and the Origin of Cutoff Frequency for Torsional TubeWaves,” ApJ, vol. 709, pp. 1297-1305, 2010.

[34] S. Routh, Z.E. Musielak and R. Hammer, “Global and local cutoff frequencies for transverse waves propagating along solar magnetic flux tubes,” ApJ, vol. 763, pp. 44, 2013.

[35] J. E. Vernazza, E. H. Avrett and R. Loeser, “Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet Sun,” ApJS, vol. 45, pp. 635, 1981.

[36] G. B. Whitman, Linear and Nonlinear Waves. Wiley, New York, 1974.

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