  Gravitational waves (GWs) generated by a first-order phase transition at the
electroweak scale are detectable by future space-based detectors like LISA. The
lifetime of the resulting shock waves plays an important role in determining
the intensity of the generated GWs. We have simulated decaying primordial
acoustic turbulence in three dimensions and make a prediction for the universal
shape of the energy spectrum by using its self-similar decay properties and the
shape of individual shock waves. The shape for the spectrum is used to
determine the time dependence of the fluid kinetic energy and the energy
containing length scale at late times. The inertial range power law is found to
be close to the classically predicted $k^{-2}$ and approaches it with
increasing Reynolds number. The resulting model for the velocity spectrum and
its decay in time is combined with the sound shell model assumptions about the
correlations of the velocity field to compute the GW power spectrum for flows
that decay in less than the Hubble time. The decay is found to bring about a
convergence in the spectral amplitude and the peak power law that leads to a
power law shallower than the $k^9$ of the stationary case.
