  We survey systematically the general parametrisations of particle-physics
models for a first-order phase transition in the early universe, including
models with polynomial potentials both with and without barriers at zero
temperature, and Coleman-Weinberg-like models with potentials that are
classically scale-invariant. We distinguish three possibilities for the
transition - detonations, deflagrations and hybrids - and consider sound waves
and turbulent mechanisms for generating gravitational waves during the
transitions in these models, checking in each case the requirement for
successful percolation. We argue that in models without a zero-temperature
barrier and in scale-invariant models the period during which sound waves
generate gravitational waves lasts only for a fraction of a Hubble time after a
generic first-order cosmological phase transition, whereas it may last longer
in some models with a zero-temperature barrier that feature severe
supercooling. We illustrate the implications of these results for future
gravitational-wave experiments.
