GENERATION OF SUBHARMONICS OF ORDER ONE-HALF BY BUBBLES IN A SOUND FIELD

Under proper conditions, bubbles driven by a sound field will pulsate periodically with a frequency equal to one half the frequency of the sound field. This frequency component is the subharmonic of order one half and is generated when the acoustic pressure amplitude exceeds a threshold value. The threshold for subharmonic generation is calculated by means of a theory that relates the presence of the subharmonic to properties of Hill's equation. It is found that, for a given bubble, the threshold is a function of the driving frequency and is a minimum when the driving frequency is approximately twice the linear resonance frequency of the bubble. In addition, solutions of a set of nonlinear equations for the motion of the bubble wall, obtained on a computer, illustrate the growth of subharmonics and are used to determine the steady state amplitude and phase of the subharmonic for a sequence of values of various parameters. © 1969, Acoustical Society of America. All rights reserved.