  The coherent manipulation of acoustic waves on the nanoscale usually requires
multilayers with thicknesses and interface roughness defined down to the atomic
monolayer. This results in expensive devices with predetermined functionality.
Nanoscale mesoporous materials present high surface-to-volume ratio and
tailorable mesopores, which allow the incorporation of chemical
functionalization to nanoacoustics. However, the presence of pores with sizes
comparable to the acoustic wavelength is intuitively perceived as a major
roadblock in nanoacoustics. Here we present multilayered nanoacoustic
resonators based on mesoporous SiO$_2$ thin-films showing acoustic resonances
in the 5-100 GHz range. We characterize the acoustic response of the system
using coherent phonon generation experiments. Despite resonance wavelengths
comparable to the pore size, we observe for the first time unexpectedly
well-defined acoustic resonances with Q-factors around 10. Our results open the
path to a promising platform for nanoacoustic sensing and reconfigurable
acoustic nanodevices based on soft, inexpensive fabrication methods.
