  We observe pronounced oscillations in differential reflectivity of 9 nm and
60 nm BaFe\textsubscript{2}As\textsubscript{2} (Ba-122) thin films using
ultrafast optical spectroscopy. Our studies show that the oscillations result
from propagating longitudinal acoustic (LA) phonon wave packets with strong
thickness and temperature dependence. Particularly, the experimentally measured
oscillation frequency approaches to 50 GHz for the ultra-thin film. Our
calculations show that Young's modulus of 9 nm thin film is nearly four times
as large as that of 60 nm thin film, consistent with the experiment. The
increase in Young's modulus as thickness decrease was attributed to the
decrease in parent Ba-122 tetragonality $c/a$ near the film-substrate interface
due to material-substrate mismatch effect. %Temperature dependence of LA phonon
mode frequency for 9 nm Ba-122 thin film is reported. The temperature-dependent
change in LA phonon frequency was attributed to the change in parent Ba-122
othorhombicity $(a-b)/(a+b)$.
