  We report temperature evolution of coherently excited acoustic and optical
phonon dynamics in superconducting iron pnictide single crystal
Ca(Fe_0.944Co_0.056)_2As_2 across the spin density wave transition at T_SDW ~
85 K and superconducting transition at T_SC ~20 K. Strain pulse propagation
model applied to the generation of the acoustic phonons yields the temperature
dependence of the optical constants, and longitudinal and transverse sound
velocities in the temperature range of 3.1 K to 300 K. The frequency and
dephasing times of the phonons show anomalous temperature dependence below T_SC
indicating a coupling of these low energy excitations with the Cooper-pair
quasiparticles. A maximum in the amplitude of the acoustic modes at T ~ 170 is
seen, attributed to spin fluctuations and strong spin-lattice coupling before
T_SDW.
