Acoustic Bubble Simulator

When a bubble forms underwater, it oscillates radially and emits sound. The Minnaert frequency gives the natural resonance of a spherical gas bubble in an infinite fluid [1]. The actual frequency accounts for proximity to the water surface (depth correction via bubble capacitance) [2].

Three damping mechanisms attenuate the oscillation: radiation (sound energy radiated away), viscous (fluid viscosity), and thermal (heat conduction between gas and liquid) [3]. A jet forcing term models the initial collapse impulse [2].

In Rising mode, the bubble ascends at its terminal velocity [4], causing a characteristic upward pitch glide as depth decreases.

The ODE is integrated at 96 kHz using a 4th-order Runge-Kutta solver, producing one second of physically accurate bubble sound.

References

1. M. Minnaert, "On musical air-bubbles and the sounds of running water," Phil. Mag., Series 7, vol. 16, no. 104, pp. 235–248, 1933. doi:10.1080/14786443309462277
2. T. R. Langlois, C. Zheng, and D. L. James, "Toward Animating Water with Complex Acoustic Bubbles," ACM Trans. Graph. (SIGGRAPH 2016), vol. 35, no. 4, pp. 1–13, July 2016. doi:10.1145/2897824.2925904 · Project page
3. T. G. Leighton, The Acoustic Bubble. Academic Press, 1994. ISBN: 9780124419209. Publisher page
4. S. Baz-Rodríguez, A. Aguilar-Corona, and A. Soria, "Rising Velocity for Single Bubbles in Pure Liquids," Rev. Mex. Ing. Quím., vol. 11, no. 2, pp. 269–278, 2012. Paper