Bubble size measurements using the nonlinear mixing of two frequencies

A double frequency method of measuring bubble size which has better spatial resolution than previous techniques, is described. Bubbles are insonified simultaneously by a swept, relatively low, ‘‘pumping’’ frequency near their resonance and a high ‘‘imaging’’ frequency. Theoretical expressions are derived for the sound scattered by a bubble under the influence of these two frequencies. Existence of sharp resonance behavior in the scattered sound at the sum frequency is shown both theoretically and experimentally.