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It is shown that the acoustic scaling patterns of anisotropic flow fordifferent event shapes at a fixed collision centrality (shape-engineeredevents), provide robust constraints for the event-by-event fluctuations in theinitial-state density distribution from ultrarelativistic heavy ion collisions.The empirical scaling parameters also provide a dual-path method for extractingthe specific shear viscosity $(\eta/s)_\mathrm{QGP}$ of the quark-gluon plasma(QGP) produced in these collisions. A calibration of these scaling parametersvia detailed viscous hydrodynamical model calculations, gives$(\eta/s)_\mathrm{QGP}$ estimates for the plasma produced in collisions ofAu+Au ($\sqrt{s_{NN}}= 0.2$ TeV) and Pb+Pb ($\sqrt{s_{NN}}= 2.76$ TeV). Theestimates are insensitive to the initial-state geometry models considered.

Acoustic scaling of anisotropic flow in shape-engineered events:  implications for extraction of the specific shear viscosity of the quark  gluon plasma