At a far enough distance it does behave exactly the same as acoustic waves.

"In particular, shock waves travel faster than sound, and their speed increases as the amplitude is raised; but the intensity of a shock wave also decreases faster than does that of a sound wave, because some of the energy of the shock wave is expended to heat the medium in which it travels. The amplitude of a strong shock wave, as created in air by an explosion, decreases almost as the inverse square of the distance until the wave has become so weak that it obeys the laws of acoustic waves."