Propagation of Acoustic-Gravity Waves from a Small Source in an Isothermal Atmosphere

Abstract

A theoretical discussion is presented of the influence of gravity on sound propagation from a point source in an isothermal atmosphere, where ambient pressure and density decrease exponentially with height. A previous theory by Sretenskii [Izv. Akad. Nauk. SSSR Ser. Geofiz. (1954)] is found to be incorrect. Our study shows that, if reflections from the gound are ignored, waves with angular frequencies between (γ − 1)12g/c and (γ/2)g/c and between 0 and (γ − 1)12(g/c) cosθ will not be propagated in a direction making an angle of θ with the vertical axis. When appropriate boundary conditions at the ground are included, the solution appears as a sum of a direct wave, a reflected wave, and a surface wave. Reflection coefficients for the reflected wave are given, and the magnitude of the surface wave as a function of horizontal distance is discussed.