ON THE VALIDITY OF THE HEURISTIC RAY-TRACE-BASED MODIFICATION TO THE WEYL-VANDERPOL FORMULA

The Weyl-Van der Pol formula from electromagnetic wave propagation the ory is known to give tolerable predictions of sound levels over a wide range of ground surfaces in a homogeneous atmosphere. A ray-tracing t echnique is perhaps the simplest approach to extend the applicability of the Weyl-Van der Pol formula to the inhomogeneous situation. Essent ially one uses ray theory to determine the path lengths and the angle of incidence at the ground. These modified parameters are then substit uted into the Weyl-Van der Pol formula for the overall sound levels. T his heuristic approach may be criticized for its lack of mathematical rigor even though it is physically reasonable. By using a ray theory a pproximation in the wave equation, a closed-form solution has been obt ained for the sound field over an impedance plane in the presence of a sound-speed gradient. It has been shown that the heuristic formula re presents an approximation of the solution. The theory also suggests th at there is a strong interaction between the sound-speed profile and t he ground surface, in particular, when the impedance is high. The solu tion is limited to a single reflection.