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Mar 1999

Volume 105, Issue 3, pp. i-2053

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Oscillations in harmonics generated by the interaction of acoustic beams

Mark D. Cahill and Andrew C. Baker

J. Acoust. Soc. Am. Volume 105, Issue 3, pp. 1575-1583 (1999); (9 pages)

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A numerical model of nonlinear propagation is used to investigate two cases of monochromatic ultrasonic beams interacting at small angles in a nonlinear medium. Two finite Young’s slits are seen to produce fringes at harmonic frequencies of the source in places where the source frequency is absent, which can be seen as a combination of harmonic generation near the source, and in the beam. Two intersecting beams with shaded edges are seen to produce similar fringes in the near field, with an oscillatory structure. Algebraic solutions to a simplified model, using the weak-field Khokhlov–Zabolotskaya equation, are invoked to illustrate the origin of the oscillations, and of the far-field directivity, providing an alternative view of the fringes due to Young’s slits. It is seen that two weakly interacting beams can produce fringes of second harmonic where the source frequency has low amplitude, if the beams coincide at the point of observation, or if a boundary condition is imposed on the second harmonic where the beams coincide. © 1999 Acoustical Society of America.
Show PACS
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.25.Jh Reflection, refraction, interference, scattering, and diffraction of intense sound waves

Theory of the backscattering of sound by phase-matched nonlinear interaction

Dmitrii Kouznetsov and Augusto García-Valenzuela

J. Acoust. Soc. Am. Volume 105, Issue 3, pp. 1584-1591 (1999); (8 pages)

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The nonlinear interaction of noncollinear acoustical waves is considered. Conditions of the resonant backscattering of one wave from the lattice produced by the other two are formulated in analogy with the four-wave mixing known in optics. The efficiency of the phase-matched interaction of acoustical waves is calculated in the resonant approximation for a gas media. Such approximation is constructed on the basis of the expansion of the sound equations preserving up to cubic terms. The amplitude of the backscattered wave is expressed as the product of the efficiency, the amplitudes of three waves, the wave number of the backscattered wave, and the size of the region of interaction. Such backscattering is proposed as an acoustical remote probe. The distance to the interaction region and the amplitude of initial waves are limited by nonlinear degradation of waves due to the second-order nonlinearity. For acoustical waves with wave number 10 m−1, sources of size 1 m, and about 100 m to the interaction region, the amplitude of the backscattered wave can be about 10−10 of the atmospheric pressure. At the detection with a signal-to-noise ratio about of 10, the resolution of such method on the wind velocity may be about 1 m/s. © 1999 Acoustical Society of America.
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43.25.Jh Reflection, refraction, interference, scattering, and diffraction of intense sound waves
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