Abstract
The purpose of this study is to clarify how bubbles reduce the speed of sound in a bubbly liquid in a duct, in which a homogeneous medium can no longer be assumed. Getting inspired by the explanation for the origin of refractive indices in the field of optics, we theoretically examine pressure wave propagation in a square duct filled with a compressible liquid containing only a spherical bubble. Theoretical examination reveals that even a single bubble in a square duct can delay the phase of the input pressure wave, causing an apparent reduction in the speed of sound. Based on this result, we can define the speed of sound in a bubbly liquid under the assumption of a homogeneous medium by considering the phase delay caused by radial oscillations of bubbles aligned in the square duct in the limit of numerous bubbles.
