An important challenge for current naval research is the modernization of battleships. Their target detection system must be increasingly efficient and they must be increasingly undetectable. Due to turbulent flows and bubbles, ship wakes are a detectable acoustic signature and ship bow waves disturb sonar detection. In this work, we study sound propagation through bubble clouds in water. We have developed an experimental set-up which permits us to acquire, in synchronization, acoustical signals and optical images. The phenomenon of bubble monopole resonance in very low frequency, related to bubble size, provokes effects of strong sound damping and sound speed dispersion. These experimental results, related to theoretical results, permit to estimated sizes and concentrations of bubbles. The acquired bubble images permit to know the real bubble sizes and concentrations, in order to correlate with the experimental acoustical results. Air bubbles are generated with a high pressure water jet introduced into the host liquid medium. A hydrodynamic study is done to characterize the bubble jet. We present in this work, theoretical results establishing a complex effective wave number characterizing the sound propagation in an effective medium. All results are discussed and compared with results of others papers on this subject.