Acoustic-gravity waves from an energy source at the ground in an isothermal atmosphere

The pressure pulse generated in an isothermal atmosphere by an energy source at the ground is calculated by the method of stationary phase from an integral representation of the pressure field previously derived by the authors. The first signal to arrive at any location is a high-frequency acoustic wave, followed by a low-frequency acoustic-gravity wave. The onset of the latter is marked by a sharp front, or caustic. At any instant (after the arrival of the caustic), there are three principal frequency components at any location, the lowest of which becomes dominant as time progresses. The qualitative features of the flow and the location of the caustic are also obtained from kinematic theory. The two alternative methods are essentially equivalent, but kinematic theory seems better adapted to the case of a slightly nonuniform medium.