Abstract: We present a detailed analytical analysis of the propagation of Bogoliubov phonons on top of Bose-Einstein condensates with spatial and temporal steplike discontinuities in the speed of sound in the hydrodynamic limit. We focus on some features in the correlations patterns, in particular, of density-density correlations. The application to the study of the Hawking signal in the formation of acoustic black hole-like configurations is also discussed.