  In this letter, we study the pion momentum distribution of a coherent source
and investigate the influences of coherent emission on the pion
transverse-momentum ($p_T$) spectrum and elliptic anisotropy. With a partially
coherent source, constructed by a conventional viscous hydrodynamics model
(chaotic part) and a parameterized expanding coherent source model, we
reproduce the pion $p_T$ spectrum and elliptic anisotropy coefficient
$v_2(p_T)$ in the peripheral Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. It
is found that the influences of coherent emission on the pion $p_T$ spectrum
and $v_2(p_T)$ are related to the initial size and shape of the coherent
source, largely due to the interference effect. However, the effect of source
dynamical evolution on coherent emission is relatively small. The results of
the partially coherent source with 33% coherent emission and 67% chaotic
emission are consistent with the experimental measurements of the pion $p_T$
spectrum, $v_2(p_T)$, and especially four-pion Bose-Einstein correlations.
