Low-frequency dispersion in bubbly liquids

The low-frequency sound speed in bubbly liquids is often modeled with an approximate equation [Wood, A Textbook of Sound, 1st ed. (MacMillan, New York, 1930)] that depends primarily on the void fraction. More recent models, developed for use at the individual bubble resonance frequency, predict a small amount of dispersion in Wood’s “dispersionless” regime. We present low-frequency data and compare it to a broadband model by Commander and Prosperetti [J. Acoust. Soc. Am. 85(2), 732–746 (1989)]. The purpose is to illustrate that dispersion of the order 5% is expected and occurs in Wood’s regime, and to point out a discrepancy between the Ruggles and the Commander and Prosperetti models regarding void fraction.