Monopole acoustic emission generated by a molten metal drop in cool water

The problem of high-frequency acoustic emission generated by a spherical hot liquid drop in a cool ambient liquid (water) is considered analytically. It is assumed that the acoustic emission is generated by the motion of the vapor cold liquid interface, which is described by the Rayleigh equation for a spherical bubble. It is also assumed that the linear relationship between the saturated pressure and the temperature is governed by the Clapeyron-Clausius law, that heat transfer from the hot liquid drop to the vapor film and the liquid takes place by a radiation, and that heat transfer from the water-vapor interface to the ambient liquid takes place by conduction. Solution of the equation obtained gives an approximate radius time relationship that allows us to evaluate the kinetic enthalpy and acoustic pressure in a far field. It is shown that, in the first approximation, the spectral density of the acoustic energy emitted by such a phenomenon varies as the minus 2.7 power of the frequency and decreases by approximately 8.1 decibels per octave with a rise in frequency.