Acoustically induced transparency is an appearance of a region free of bubbles near an acoustic transducer placed into the bubbly liquid. This substantially nonlinear phenomenon happens due to two-way interaction of bubbles and the acoustic field. In this study we present a mathematical model of self-organization of bubbles in acoustic fields which describes propagation of the waves of transparency, which are nothing but void fraction shock waves. We developed one and three dimensional numerical simulators based on this model and performed numerical studies. We also developed an experimental setup and conducted experiments at different frequencies and amplitudes of acoustic waves for various liquids and gases inside the bubbles. Numerical and experimental results were compared and a good agreement was found. The discovered phenomenon should be studied more carefully due to numerous potential applications.