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La résonance de Minnaert
In 1933, M. Minnaert published a paper on "Musical Air-Bubbles and Sounds of Running Water" [1]. He observed that when 3 to 6 mm air bubbles were injected into water, they emitted a sound at a frequency of about 2 kHz (see bubble piano), i.e. in the audible range. This was a surprise, because the standard model for cavities with a solid boundary predicts a resonance at 100 kHz, non audible.
One can understand the origin of this low frequency resonance with a model of harmonic oscillator. As depicted in the figure, there is an analogy between the oscillations of a spring-bob system and the breathing mode of a gas bubble in a liquid. For the bubble, the stiffness of the spring is given by the compressiblity of air, whereas the mass depends on the inertia of water. The eigen frequency 
is thus low because the bubble is an hybrid system which takes it small stiffness from air and its large inertia from water. We have proposed simple experiments to illustrate the harmonic oscillator behavior of bubbles [2].
[1] M. Minnaert, Phil. Mag. 16, 235 (1933).
[2] V. Leroy, M. Devaud, J.-C. Bacri, Am. J. Phys. 70, 1012 (2002)
[3] M. Devaud, T. Hocquet, J.-C. Bacri, and V. Leroy, Eur. J. Phys. 29, 1263 (2008)
Contact : Published on / Publié le 4. Mai 2011
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