Interference of the direct and ground-reflected waves in the atmosphere with volumetric scatteringa)

The interference of the direct and ground-reflected sound waves is significantly affected by volumetric scattering in the atmosphere, such as scattering by turbulence and forest. In the present article, the existing theory describing this interference is generalized to three somewhat independent but equally important cases. First, the attenuation of the direct and ground-reflected waves caused by backscattering is addressed. Second, the existing theory is extended for statistically quasi-homogeneous turbulence in which the variances and length scales of the temperature and wind velocity fluctuations depend on the height above the ground. Third, the existing theory, which was previously formulated only for near-horizontal sound propagation, is generalized to slanted sound propagation as pertinent to elevated sound sources. Numerical results for slanted propagation demonstrate that atmospheric turbulence can significantly increase the sound pressure level at the interference minima. The extended theory of the interference of the direct and ground-reflected waves in the atmosphere with volumetric scattering is important for practical applications, such as auralization of flying aircraft and sound propagation in a forest, and can be adapted to radio wave propagation.