Solid phases of water, such as ice (Ih) and clathrate hydrates, form characteristic hydrogen bond network motifs, such as hexagonal ice, pentagons, and dodecahedrons. The same motifs might be present in supercooled water and in the hydration structure around hydrophobes. Here, we present the characteristic low frequency fingerprints of ice (Ih), tetrahydrofuran (THF) clathrate hydrates, and tetrabutyl-ammonium bromide (TBAB) semiclathrate close to their melting point, as well as supercooled water at 266.6 K and aqueous alcohol solutions. Interestingly, we find in all these cases two characteristic resonances in the THz frequency range: at least, one intensive band in the frequency range between 190 cm-1 and 220 cm-1 which is a characteristic of a tetrahedral hydrogen bond network configuration and a second band in the frequency range between 140 cm-1 and 170 cm-1, indicating a component with weaker hydrogen bonds. For solvated alcohols, we find spectroscopic fingerprints of a clathratelike structure at 164 cm-1 as well as a tetrahedral network structure at 194 cm-1, which is close to one of ice (Ih) at 192 cm-1. We propose that in the hydration shell of hydrophobes, both structural motifs are present. In the case of supercooled water-unlike ice-only one peak was found in the frequency range between 190 cm-1 and 220 cm-1. Interestingly, the latter peak center-frequency (204 cm-1) corresponds to the average of those of the two peaks observed for ice Ih (191 cm-1 and 215 cm-1). This indicates a homogeneous intermediate hydrogen bonding, providing no evidence for any heterogeneity in two high-density and low-density phases.