Aqueous foams are known to be excellent acoustic insulators and used as such e.g. in military context, but there is no clear physical picture even at low driving pressure. To resolve this issue, we perform systematic measurements of the speed of sound and attenuation through both commercial and home-made (based on simple usual surfactants like SDS) foams. We report mostly measurements at 40 kHz, but we also mention measurements at lower and higher frequencies, in the range 0.5-600 kHz. We quantify the influence of the bubble size a (15-200 µm), thanks to the natural coarsening of an ageing foam.

Since the acoustic wavelength is much larger than the bubble size in this parameter range, we develop a mean-field model based on the coupled dynamics of a soap film and a Plateau border, the two items constituting the liquid network of a foam. This model system displays a resonance frequency inversely proportional to the film radius. Below resonance, the film and the Plateau border oscillate similarly. Above resonance, only the films move significantly.

Our model quantitatively explains the highly dispersive and complex acoustic behaviour that our experiments reveal for the first time: low speed of sound at small frequency and bubble size; large speed of sound just below that of air at large frequency and bubble size; and a transition regime with a maximum for the speed of sound, and another one for the attenuation. This study provides new insights on wave attenuation by aqueous foams, which is of great interest to better model and optimise this process for industrial applications.