Small Oscillations of a Soap Bubble

We analyze the spectrum of small oscillations of a soap bubble surrounded by incompressible inviscid air. The analysis is based on the linearization of the exact system for the dynamics of free fluid films. The underlying model takes into account variations in the film's shape and thickness. The resulting dispersion relationship shows the fundamental interplay among these variations. In the limit of vanishing soap bubble mass, the presented dispersion relationship agrees with Rayleigh's classical formula for an oscillating liquid droplet under the influence of surface tension.