<p>Bogoliubov waves are fundamental excitations of Bose-Einstein condensates. They emerge from a perturbed ground state and interact nonlinearly, triggering turbulent cascades. Here, we study turbulent Bose-Einstein condensates theoretically and numerically using the three-dimensional Gross-Pitaevskii model and its associated wave-kinetic equations. We derive a Kolmogorov-like stationary spectrum for short Bogoliubov waves and find a complete analytical expression for the spectrum in the long-wave acoustic regime. We then use our predictions to explain the far-from-equilibrium equation of state observed in recent turbulent quantum gas experiments, and to suggest future experimental settings.</p>