Analytical Stationary Acoustic Wave in a Liquid over Which a Moving Pressure Runs

Abstract

This paper presents an analytical study of the stationary response of a liquid loaded on its free surface by an ideal pressure step moving in a constant direction at a constant velocity. The acoustic pressure in the liquid is found, in four different examples, by means of the Fourier Transform. Two loading regimes are considered; subsonic and supersonic. Two configurations of liquid domains are also studied, the first one is a half infinite space while the second one is bounded by a rigid bottom at a finite depth. For the two supersonic cases, a simple reasoning based on the existence of a front of discontinuity in the liquid and on the property of reflection of waves confirms the result of the mathematical investigations. The results obtained for the steady state case are of intererest, even when the loading is not exactly stationary, such as the presure produced by an explosion occurring in the vicinity of the surface of a liquid. Two numerically resolved examples are presented, which confirm this assumption.For the two supersonic cases, a simple reasoning based on the existence of a front of discontinuity in the liquid and on the property of reflection of waves confirms the result of the mathematical investigations.The results obtained for the steady state case are of intererest, even when the loading is not exactly stationary, such as the presure produced by an explosion occurring in the vicinity of the surface of a liquid. Two numerically resolved examples are presented, which confirm this assumption.