Generation of Subharmonics of Order One-Half by Bubbles in a Sound Field

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Abstract
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 1 2 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 Mathieu'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 close to twice the resonance frequency of the bubble. In addition, solutions of a nonlinear equation of motion for the bubble wall, obtained on a computer, illustrate the growth of subharmonics and are used to determine the steady‐state amplitude of the subharmonic for a sequence of values of various parameters. [Work supported by Acoustics Programs, Office of Naval Research.]

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