Fine structure of transient waves in a random medium: The half N wave

Abstract

The propagation of a transient scalar wave in a one-dimensional random medium is considered. The initial disturbance is assumed to have a bilinear form characterized by a relatively short compression phase followed by a relatively long expansion phase. A wave having such a form is referred to here as a half N wave. Based on a general formula derived previously, an expression for the variance, which is a measure of the fine structure, of the half N wave is obtained. In a region encompassing the compression phase and the initial portion of the expansion phase of the wave, the behavior of the fine structure, as determined by this expression, is found to be consistent with observations of actual transient waves, such as sonic booms. Further into the expansion phase, however, discrepancies between theory and observations appear. These findings are described in detail. [Research supported by NASA.]