Infrasonic wave propagation in ultrasoft solids at low Reynolds numbers

The propagation of elastic waves in soft materials plays a crucial role in the spatio-temporal transmission of mechanical signals, e.g. in biological mechanotransduction or in the failure of marginal solids. At high Reynolds numbers $Re \gg 1$, inertia dominates and wave propagation can be readily observed. However, mechanical cues in soft and biological materials often occur at low $Re$, where waves are overdamped. Not only have low $Re$ waves been difficult to observe in experiments, their theoretical description remains incomplete. In this paper, we present direct measurements of low $Re$ waves propagating in ordered and disordered soft solids, generated by an oscillating point force induced by an optical trap. We derive an analytical theory for low $Re$ wave propagation, which is in excellent agreement with the experiments. Our results present both a new method to characterize wave propagation in soft solids and a theoretical framework to understand how localized mechanical signals can provoke a remote and delayed response.