  Arising out of a Non-local non-relativistic BEC, we present an Analogue
gravity model upto $\mathcal{O}(\xi^{2})$ accuracy in the presence of the
quantum potential term for a canonical acoustic BH in $(3+1)$-d spacetime where
the series solution of the free minimally coupled KG equation for the large
length scale massive scalar modes is derived. We systematically address the
issues of the presence of the quantum potential term being the root cause of a
UV-IR coupling between short wavelength `primary' modes which are supposedly
Hawking radiated through the sonic horizon and the large wavelength `secondary'
modes. In the quantum gravity experiments of analogue Hawking radiation in the
laboratory, this UV-IR coupling is inevitable and one can not get rid of these
large wavelength excitations which would grow over space by gaining energy from
the short wavelength Hawking radiated modes. We identify the characteristic
feature in the growth rate(s) that would distinguish these primary and
secondary modes.
