Could you please explain the general theory behind the sound that is produced when water falls on a hot surface?
To begin with, sound (or the propagation of sound) occurs via a pressure wave. When water (or in general, when a liquid heats up) it's vapor pressure increases. Vapor pressure can sort of be described as the pressure exerted by the particles in a liquid by their kinetic energy in opposition to atmospheric pressure. When the vapor pressure increases to greater than the atmospheric pressure, boiling occurs. At one atmosphere of pressure (760 torr, etc) this occurs at 100 C. When water is poured on a surface that is sufficiently hot to heat water to its boiling temperature on a timescale that is (or appears to be) instantaneous, one can imagine that there would be a very hot local environment around the surface. One would also imagine that the temperature gradient would fall off fairly quickly as a function of distance so that the ambient temperature and pressure can be said to not be affected by the surface. However, this environment would be sufficient to further heat (and increase the pressure) of the water vapor boiling off of the surface. This rapid increase in pressure relative to the atmospheric pressure creates a pressure gradient which propagates as a sound wave, which is why you hear sound from the boiling water. You do not hear the same sound from a pot of boiling water because there is not the same rapid heating of the water vapor creating the large pressure difference between vapor and atmosphere.
Jay Foley, None, Chemistry Undergrad, GA Tech
'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'