  Elucidating the nature of spin excitations is important to understanding the
mechanism of superconductivity in the iron pnictides. Motivated by recent
inelastic neutron scattering measurements in the nearly 100% detwinned
BaFe$_{2}$As$_{2}$, we study the spin dynamics of an $S=1$ frustrated
bilinear-biquadratic Heisenberg model in the antiferromagnetic phase with
wavevector $(\pi,0)$. The biquadratic interactions are treated in a dynamical
way using a flavor-wave theory in an $SU(3)$ representation. Besides the magnon
(dipolar) excitations, the biquadratic interactions give rise to quadrupolar
excitations at high energies. We find that the quadrupolar wave significantly
influences, in an energy dependent way, the anisotropy between the spin
excitation spectra along the $(\pi,0)$ and $(0,\pi)$ directions in the wave
vector space. Our theoretical results capture the essential behavior of the
spin dynamics measured in the antiferromagnetic phase of the detwinned
BaFe$_2$As$_2$. More generally, our results underscore the importance of
electron correlation effects for the microscopic physics of the iron pnictides.
