The oscillations of a small floating bubble

A simple model of a small bubble floating at the surface of a liquid before bursting is considered. The oscillations of this system are studied by means of a Lagrangian method. It is found that two fundamentally different modes exist. The surface mode has low frequency and does not change appreciably the volume of the immersed part of the bubble: As a consequence, its efficiency as a source of sound in the water is very limited. The volume mode has a much higher frequency and is a more efficient radiator in the water, although it may be hard to excite. Both modes behave as monopole sources in the air. It is therefore predicted that an oscillating floating bubble is a much more intense source of sound in the air than in the liquid. This conclusion seems to be supported by experimental observations.