  Exciton-polaritons in semiconductor microcavities constitute the archetypal
realization of a quantum fluid of light. Under coherent optical drive,
remarkable effects such as superfluidity, dark solitons or the nucleation of
hydrodynamic vortices have been observed. These phenomena can be all understood
as a specific manifestation of collective excitations forming on top of the
polariton condensate. In this work, we performed a Brillouin scattering
experiment to measure their dispersion relation $\omega(\mathbf{k})$ directly.
The result, such as a speed of sound which is apparently twice too low, cannot
be explained upon considering the polariton condensate alone. In a combined
theoretical and experimental analysis, we demonstrate that the presence of a
reservoir of long-lived excitons interacting with polaritons has a dramatic
influence on the nature and characteristic of the quantum fluid, and that it
explains our measurement quantitatively. This work clarifies the role of such a
reservoir in the different polariton hydrodynamics phenomena occurring under
resonant optical drive. It also provides an unambiguous tool to determine the
condensate-to-reservoir fraction in the quantum fluid, and sets an accurate
framework to approach novel ideas for polariton-based quantum-optical
applications.
