The model:
The natural frequency and damping of a
bubble, when it is modelled as a lightly damped oscillator, have been
available in the literature for many decades (note however that these
expressions are valid only for monochromatic free field emissions - this
point will be re-examined at the end of this presentation). Some of the
earliest references are:
Minnaert, M. On musical air-bubbles and sounds of running water, Phil. Mag. 1933; 16: 235-248.
Devin, C. Jr., Survey of Thermal, Radiation, and Viscous Damping of Pulsating Air Bubbes in Water. J. Acoust. Soc. Am. 1959; 31: 1654
 |
where
the d terms are the dimensionless damping coefficients for thermal (th),
viscous (vis), acoustic radiation (rad) and any other (other)
sources of energy loss. Their sum dtot is the reciprocal
of the quality factor of the bubble. (Click here if you wish to jump ahead to see how these parameters are modified by reverberation) |
| Click here for previous page |