Reduction in the Propagation Speed of Linear Pressure Wave in a Square Duct Filled with a Compressible Liquid Containing Multiple Spherical Bubbles*

Pressure wave propagation in a bubbly liquid causes oscillations of bubbles dispersed in a liquid medium. The bubble oscillations affect profoundly the propagation speed of pressure wave in the medium. As the acoustic characteristics of a liquid affected by bubble oscillations, it is well known that the speed of sound in a bubbly liquid is lower than that in a pure liquid. A number of investigators explained the mechanism of the reduction in the speed of sound in a bubbly liquid, in which a homogeneous medium could be assumed. The aim of our study is to investigate the propagation speed of pressure wave in a bubbly liquid in a square duct, in which a homogeneous medium can no longer be assumed. Getting inspired by Feynman’s study, we theoretically examine linear pressure wave propagation in a square duct filled with a compressible liquid containing multiple spherical bubbles. The present study reveals the mechanism of the reduction in the speed of sound caused by bubble oscillations in a square duct without the continuum assumption in a bubbly liquid.