  Ultra-light scalar fields and their non-interacting class, the so-called
fuzzy dark matter (FDM), are candidates for dark matter, introduced to solve
the small-scale problems of the standard cold dark matter. In this paper, we
address whether the small-scale effects, specifically the quantum pressure,
could leave sizable imprints on the large-scale statistics of the matter. For
this purpose, We utilize the Effective Field Theory of Large Scale Structures
(EFT of LSS) wherein small-scale physics is integrated and represented on large
scales by only a set of free parameters. These parameters can be determined by
fitting to the cosmological simulations. We use the \textit{Gadget-2} code to
study the evolution of $512^3$ particles in a box of side length
$250\,h^{-1}\,\mathrm{Mpc}$. Fitting EFT predictions to the simulation data, we
determine the value of the speed of sound. We use the suppressed FDM initial
conditions for the FDM case, sufficient to produce accurate -- enough for our
purpose -- results on large scales. We perform three FDM simulations with
different masses and compare their sound speed with the standard cold dark
matter (CDM) simulation. We found that the FDM sound speed is slightly higher
than CDM's. The deviation of the sound speed for FDM from CDM is larger for
lower FDM masses. We conclude that the impact of the FDM is not limited to the
small scales alone, and we can search for them by studying the matter on large
scales. Though it is beyond the observations' scope today, it is possible to
discriminate it with upcoming observations.
