  Equilibrium molecular dynamics simulations are performed to study
two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal
motion of simulated particles, the longitudinal and transverse phonon spectra
are calculated, and used to determine the corresponding dispersion relations.
From there, the longitudinal and transverse sound speeds of 2D dusty plasma
liquids are obtained. It is discovered that, for wavenumbers beyond the
hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid
exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon
appears at roughly the same length scale of the cutoff wavenumber for
transverse waves, confirming its relation to the emergent solidity of liquids
in the non-hydrodynamic regime. Using the thermodynamic and transport
coefficients extracted from the previous studies, and relying on the Frenkel
theory, the ratio of the longitudinal to the adiabatic sound speeds is derived
analytically, providing the optimal conditions for fast sound, which are in
quantitative agreement with the current simulation results.
