On the impact noise of a drop falling on water

An analysis is made of the impact sound generated when a water droplet impinges on a nominally smooth air–water interface. Guo and Ffowcs Williams [Journal of Fluid Mechanics 227 (1991) 345–355] derived a mathematical representation of the sound produced in the initial period of impact of duration ⪡ 1 μ s . The theory of this paper is a simple extension of their method that covers all of the effective life time ( ∼ 100 μ s ) of the impact sound pulse. At the acoustic wavefront the predicted pressure signature in the water consists of a large impulsive peak with the directivity of an acoustic monopole source. Behind this peak lower frequency components of the sound are strongly influenced by the effective pressure-release condition on the free surface of the water, and the radiation acquires the characteristics of a much weaker dipole field (with dipole axis normal to the water interface) accompanied by a rapid decrease in wave amplitude. The dipole pressure exhibits a single cycle oscillation before decaying to evanescence about 0.1 ms after the initial impact. Predictions of the acoustic pressure spectral level are shown to be consistent with measurements available in the literature. Applications of the theory are envisaged to situations where the entrainment of air bubbles by droplets is not important, so that the impact is the dominant source of sound—for example, in estimating the contribution to the self-noise of a supercavitating vehicle from ventilating gas containing a ‘spray’ of small droplets impinging on the cavity gas–water interface.