Plenary lecture IV - On the sound propagation in the open air

This contribution is planned to provide the application of the soliton theory to understand the sound propagation in the open air. The sound propagation in the atmosphere is more complicated than the theory of geometrical spreading above a. flat hard ground. When sound propagates, it is attenuated with increasing distance between source and receiver, and the sound characteristics depend on time and the distance from the source. Grounds may not be flat and also acoustically soft, the wind and temperature refract sound either upwards or downwards at the ground, leading to complex reflection coefficients and the multiple reflections at the ground. Atmospheric turbulence causes fluctuations and scatters sound into acoustical shadow zones. The methodology to study the sound evolution equation is the soliton theory. The sound is regarded as an entity, a quasi-particle, characterized by a proper propagation mechanism which conserves its character and interacts with the ground properties and micrometeorological factors. The sound propagation theory is faced with the unexpected appearance of chaos or order. Within this framework the soliton plays the role of order. The results obtained in the linear theory of sound motion, by ignoring the nonlinear parts, are most frequently too far from reality to be useful. The linearization misses an important phenomenon, solitons, which are waves, which maintain their identity indefinitely just when we most expect that dispersion effects will lead to their disappearance. The solutions regarding the attenuation due to atmospheric absorption, the decrease in sound pressure level with different factors, are represented by the revolution ruled Tzitzeica surfaces. The capability of the Backlund transformation to provide an integrable discretization of the characteristic equations associated to the sound propagation, are considered for modeling the sound rays during downwind and upwind propagation.