Sounds and hydrodynamics of polar active fluids

Spontaneously flowing liquids have been successfully engineered from a variety of biological and synthetic self-propelled units(1-11). Together with their orientational order, wave propagation in such active fluids has remained a subject of intense theoretical studies(12-17). However, the experimental observation of this phenomenon has remained elusive. Here, we establish and exploit the propagation of sound waves in colloidal active materials with broken rotational symmetry. We demonstrate that two mixed modes, coupling density and velocity fluctuations, propagate along all directions in colloidal-roller fluids. We then show how the six material constants defining the linear hydrodynamics of these active liquids can be measured from their spontaneous fluctuation spectrum, while being out of reach of conventional rheological methods. This active-sound spectroscopy is not specific to synthetic active materials and could provide a quantitative hydrodynamic description of herds, flocks and swarms from inspection of their large-scale fluctuations(18-21).