  We numerically demonstrate atomic Fabry-Perot resonances for a pulsed
interacting Bose-Einstein condensate (BEC) source transmitting through double
Gaussian barriers. These resonances are observable for an
experimentally-feasible parameter choice, which we determined using a
previously-developed analytical model for a plane matter-wave incident on a
double rectangular barrier system. By simulating an effective one-dimensional
Gross-Pitaevskii equation, we investigate the effect of atom number, scattering
length, and BEC momentum width on the resonant transmission peaks. For
$^{85}$Rb atomic sources with the current experimentally-achievable momentum
width of $0.02 \hbar k_0$ [$k_0 = 2\pi/(780~\text{nm})$], we show that
reasonably high contrast Fabry-Perot resonant transmission peaks can be
observed using a) non-interacting BECs of $10^5$ atoms, b) interacting BECs of
$10^5$ atoms with $s$-wave scattering lengths $a_s=\pm 0.1a_0$ [$a_0$ is the
Bohr radius], and c) interacting BECs of $10^3$ atoms with $a_s=\pm 1.0a_0$.
Our theoretical investigation impacts any future experimental realisation of an
atomic Fabry-Perot interferometer with an ultracold atomic source.
