Numerical investigation of transmission of low frequency sound through a smooth air-water interface

Abstract

It is the traditional belief that sound transmission from water to the air is very weak due to a large contrast between air and water impedances. Recently, the enhanced sound transmission and anomalous transparency of air-water interface have been introduced. Anomalous transparency of air-water interface states that the sound generated by a submerged shallow depth monopole point source localized at depths less than 1/10 sound wavelength, can be transmitted into the air with omni-directional pattern. The generated sound has 35 times higher power compared to the classical ray theory prediction. In this paper, sound transmission through air-water interface for a localized underwater shallow depth source is examined. To accomplish this, two-phase coupled Helmholtz wave equations in two-phase media of air-water are solved by the commercial finite element based COMSOL Multiphysics software. Ratios of pressure amplitudes of different sound sources in two different underwater and air coordinates are computed and analyzed against non-dimensional ratio of the source depth (D) to the sound wavelength (λ). The obtained results are compared with the experimental data and good agreement is displayed.

Keywords

enhanced sound transmission / anomalous transparency / air-water interface / shallow depth source / sound transmission / Helmholtz wave equations

References

[1] Bayliss A, Gunzburger M, Turkel E. Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM Journal on Applied Mathematics, 1982, 42(2): 430-451

[2] Brokesova J. Reflection/transmission coefficients at a plane interface in dissipative and nondissipative isotropic media: a comparison. Journal of Computational Acoustics, 2001, 9(2): 623-641

[3] Buckingham MJ. Precision correlations between the geoacoustic parameters of an unconsolidated sandy marine sediment. Journal of Computational Acoustics, 2001, 9(1): 101-123

[4] Buckingham MJ, Garcés MS. Airborne acoustics of explosive volcanic eruptions. Journal of Computational Acoustics, 2001, 9(3): 1215-1225

[5] Buckingham MJ, Giddens EM, Simonet F, Hahn TR. Propeller noise from a light aircraft for low frequency measurements of the speed of sound in a marine sediment. Journal of Computational Acoustics, 2002, 10(4): 445-464

[6] Calvo DC, Nicholas M, Orris GJ. Experimental verification of enhanced sound transmission from water to air at low frequencies. Journal of Acoustical Society of America, 2013, 134(5): 3403-3408

[7] Carey WM, Lynch JF, Siegmann WL, Rozenfeld I, Sperry BJ. Sound transmission and spatial coherence in selected shallow-water areas: measurements and theory. Journal of Computational Acoustics, 2006, 14(2): 265-298

[8] Cheng HK, Lee CJ. Sonic-boom noise penetration under a wavy ocean: Theory. Journal of Fluid Mechanics, 2004, 514: 281-321

[9] DeSanto JA. Derivation of the acoustic wave equation in the presence of gravitational and rotational effects. Journal of Acoustical Society of America, 1979, 66(3): 827-830

[10] Desharnais F, Chapman DMF. Underwater measurements and modeling of a sonic boom. Journal of Acoustical Society of America, 2002, 111(1): 544-553

[11] Etter PC. Underwater acoustic modeling and simulation, 2003, Third ed., Spon Press, Taylor & Francis Group: London and New York

[12] Ferguson BG. Doppler effect for sound emitted by a moving airborne source and received by acoustic sensors located above and below the sea surface. Journal of Acoustical Society of America, 1993, 94(6): 3244-3247

[13] Ghadimi P, Bolghasi A, Feizi Chekab MA. Acoustic simulation of scattering sound from a more realistic sea surface: consideration of two practical underwater sound sources. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2014

[14] Ghadimi P, Bolghasi A, Feizi C M. Low frequency sound scattering from rough bubbly ocean surface: Small perturbation theory based on the reformed Helmholtz- Kirchhoff-Fresnel method. Journal of Low Frequency Noise, Vibration and Active Control, 2014, 34(1): 49-72

[15] Godin OA. Anomalous transparency of water-air interface for low frequency sound. Phys. Rev. Lett., 2006, 97: 164301

[16] Godin OA. Transmission of low-frequency sound through the water-to-air interface. Acoustical Physics, 2007, 53(3): 353-361

[17] Godin OA. Low-frequency sound transmission through a gas-liquid interface. Journal of Acoustical Society of America, 2008, 123(4): 1866-1879

[18] Godin OA. Sound transmission through water-air interfaces: new insights into an old problem. Contemporary Physics, 2008, 49(2): 105-123

[19] Goodman RR, Farwell RW. A note on the derivation of the wave equation in an inhomogeneous ocean. Journal of Acoustical Society of America, 1979, 66(6): 1895-1896

[20] Gordienko VA, Gordienko EI, Zakharov LN, Il’ichev VI. The shallow-water propagation particularities of the signals transduced by source located above water-surface. Doklady Akad. Nauk, 1993, 333(4): 503-506

[21] Kazandjian L, Leviandier L. A normal mode theory of air-to-water sound transmission by a moving source. Jourl of Acoustical Society of America, 1994, 96(3): 1732-1740

[22] Kinsler LE, Frey AR, Coppens AB, Sanders JV. Fundamentals of Acoustics, 1982, hird ed., John Wiley & Sons: New York.

[23] Komissarova NN. Sound field features in the coastal zone of a shallow sea with an airborne source of excitation. Acoustical Physics, 2001, 47(3): 313-322

[24] Lubard SC, Hurdle PM. Experimental investigation of acoustic transmission from air into a rough ocean. Journal of Acoustical Society of America, 1976, 60(5): 1048-1052

[25] McDonald BE, Calvo DC. Enhanced sound transmission from water to air at low frequencies. Journal of Acoustical Society of America, 2007, 122(6): 3159-3161

[26] Medwin H, Clay CS. Fundamentals of acoustical oceanography, 1998, Academic Press: Boston

[27] Ravazzoli CL. Analysis of the reflection and transmission coefficients in three-phase sandstone reservoirs. Journal of Computational Acoustics, 2001, 9(4): 1437-1454

[28] Richardson WJ, Greene CR, Malme Jr C, Thomson DH. Marine mammals and noise, 1995, Academic Press: New York

[29] Sparrow VW. Review and status of sonic boom penetration into the ocean. Journal of Acoustical Society of America, 2002, 111(1): 537-543

[30] Sohn RA, Vernon F, Hildebrand JA, Webb SC. Field measurements of sonic boom penetration into the ocean. Journal of Acoustical Society of America, 2000, 107(6): 3073-3083

[31] Temkin S. Elements of Acoustics, 2001, Wiley: New York.