A theoretical study on drop impact sound and rain noise

Abstract

This paper examines the sound waves generated when a spherical water drop impacts upon an initially quiescent water surface. The pressure fluctuations and the acoustic energy radiated by the initial impact are calculated analytically. It is shown that the rapid momentum exchange between the fluid in the falling drop and that in the main water body causes the radiation of compressive waves. These waves are radiated in the form of a wave packet with a densely packed edge which is heard in the far field as a noisy shock-like pulse followed by a quickly decreasing tail. The wave packet carries with it sound energy proportional to the kinetic energy of the falling drop and to the cube of the impact Mach number. Applications of these analytic results to the study of noise from natural rain are discussed, and an illustrative example is given where the noise level due to rain showers is linearly related to the rainfall rate, which is shown to be consistent with observations.