  In this paper, we analyse sound waves arising from a cosmic phase transition
where the full velocity profile is taken into account as an explanation for the
gravitational wave spectrum observed by multiple pulsar timing array groups.
Unlike the broken power law used in the literature, in this scenario the power
law after the peak depends on the macroscopic properties of the phase
transition, allowing for a better fit with pulsar timing array (PTA) data. We
compare the best fit with that obtained using the usual broken power law and,
unsurprisingly, find a better fit with the gravitational wave (GW) spectrum
that utilizes the full velocity profile. We then discuss models that can
produce the best-fit point and complementary probes using CMB experiments and
searches for light particles in DUNE, IceCUBE-Gen2, neutrinoless double beta
decay, and forward physics facilities at the LHC like FASER nu, etc.
