Modeling frequency shifts of collective bubble resonances with the boundary element method.

Increasing the number of closely packed air bubbles immersed in water changes the frequency of the Minnaert resonance. The collective interactions between bubbles in a small ensemble are primarily in the same phase, causing them to radiate a spherically symmetric field that peaks at a frequency lower than the Minnaert resonance for a single bubble. In contrast, large periodic arrays include bubbles that are further apart than half of the wavelength such that collective resonances have bubbles oscillating in opposite phases, ultimately creating a fundamental resonance at a frequency higher than the single-bubble Minnaert resonance.