Mathematical model for volcanic harmonic tremors

Harmonic tremors consist in the release of infrasonic energy associated with volcanic activity. The typical frequency range of harmonic tremors is 0.1-12 Hz. We suppose that the harmonic tremors are due to the formation of bubbles entrapped in cavities that oscillate converting thermal energy into mechanic energy. Reproducing the natural phenomenon through an experimental apparatus, we propose here a mathematical model to describe the oscillatory mechanism and to detect the frequency as a function of the main physical parameters. We show that the frequency obtained through the model is in agreement with the one obtained through experimental measurements and with the data available from the literature, proving the consistency of the proposed model.