Certain holographic states of matter with a global U(1) symmetry support a sound mode at zero temperature, caused neither by spontaneous symmetry breaking of the global U(1) nor by the emergence of a Fermi surface in the infrared. In this work, we show that such a mode is also found in zero density holographic quantum critical states. We demonstrate that in these states, the appearance of a zero temperature sound mode is the consequence of a mixed `t Hooft anomaly between the global U(1) symmetry and an emergent higher-form symmetry. At non-zero temperatures, the presence of a black hole horizon weakly breaks the emergent symmetry and gaps the collective mode, giving rise to a sharp Drude-like peak in the electric conductivity. A similar gapped mode arises at low temperatures for non-zero densities when the state has an emergent Lorentz symmetry, also originating from an approximate anomalous higher-form symmetry. However, in this case the collective excitation does not survive at zero temperature where, instead, it dissolves into a branch cut. We comment on the relation between our results and the application of the Luttinger theorem to compressible holographic states of matter.