Acoustic wave speed in aerogels across material classes: density scaling from theory and experiments

Understanding the propagation of elastic waves in ultra-light porous solids is essential for linking their microstructure to macroscopic properties and mechanical performance. In this work, we present first an experimental study of longitudinal sound velocity in aerogels spanning a wide range of chemical structures and mesoscopic architectures, including polyurethane, polylactic acid, polyimide, flexible organo-silica, classical silica, and phenolic (resorcinol-formaldehyde) aerogels. Compression wave velocities were measured and correlated with bulk density to establish scaling relations across aerogel material families. While classical elasticity implies direct coupling between sound velocity in isotropic solids and elastic moduli, we then examine the extent to which such continuum relations remain valid in aerogels, whose structure is governed by hierarchical porosity, nanoscale connectivity, and bending-dominated network mechanics. Finally, we suggest measuring the Young modulus of aerogels from the acoustic wave speed as a non-destructive testing alternative.