(Abridged) Aims: We characterize the dynamics of the quiet inter-network chromosphere by studying the occurrence of acoustic shocks and their relation with the concomitant photospheric structure and dynamics. Methods: We analyze a comprehensive data set that includes high resolution chromospheric and photospheric spectra obtained with the IBIS imaging spectrometer in two quiet-Sun regions. This is complemented by high-resolution sequences of MDI magnetograms of the same targets. From the chromospheric spectra we identify the spatio-temporal occurrence of the acoustic shocks. We compare it with the photospheric dynamics by means of both Fourier and wavelet analysis, and study the influence of magnetic structures. Results: Mid-chromospheric shocks occur as a response to underlying powerful photospheric motions at periodicities nearing the acoustic cut-off, consistent with 1-D hydrodynamical modeling. However, their spatial distribution within the supergranular cells is highly dependent on the local magnetic topology, both at the network and internetwork scale. Large portions of the internetwork regions undergo very few shocks, as shadowed by the horizontal component of the magnetic field. The latter is betrayed by the presence of chromospheric fibrils, observed in the core of the CaII line as slanted structures with distinct dynamical properties. The shadow mechanism appears to operate also on the very small scales of inter-network magnetic elements, and provides for a very pervasive influence of the magnetic field even in the quietest region analyzed.
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