The recent progress in the context of elastic metamaterials and modulated waveguides with digitally controllable properties has spurred the research in the context of time-varying and space-time varying mechanical systems. In other words, the search of new functionalities, such as nonreciprocity, frequency conversion, parametric amplification, and edge-to-edge pumping, to name a few, requires advanced space-time control of the material parameters, which justifies the emergence of active times in phononics. The work presented herein discusses temporal modulations in the context of stiffness-modulated elastic structures, with emphasis on frequency conversion and wave steering. It is shown that slow temporal modulations, compliant with the adiabatic theorem, can be functionally employed to change the frequency content and the propagation direction of incident wave packets. At the same time, adiabatic variations avoid the scattering of back-propagating waves, which are instead present in case of fast modulations and, in many cases, can be undesired from a practical perspective. Both transient and steady-state behaviors of stiffness-modulated waveguides are discussed with the goal of achieving controllable transmission of elastic signals between an emitter and a receiver.