Volume 105, Issue 3, March 1999
Index of content:
- NONLINEAR ACOUSTICS 
105(1999); http://dx.doi.org/10.1121/1.426697View Description Hide Description
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.
105(1999); http://dx.doi.org/10.1121/1.426698View Description Hide Description
The nonlinear interaction of noncollinear acoustical waves is considered. Conditions of the resonantbackscattering 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-matchedinteraction 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 backscatteredwave is expressed as the product of the efficiency, the amplitudes of three waves, the wave number of the backscatteredwave, 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 backscatteredwave can be about 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.