  We use a new quenching scheme to study the dynamics of a one-dimensional
anisotropic $XY$ spin-1/2 chain in the presence of a transverse field which
alternates between the values $h+\de$ and $h-\de$ from site to site. In this
quenching scheme, the parameter denoting the anisotropy of interaction ($\ga$)
is linearly quenched from $-\infty$ to $ +\infty$ as $\ga = t/\tau$, keeping
the total strength of interaction $J$ fixed. The system traverses through a
gapless phase when $\ga$ is quenched along the critical surface $h^2 = \de^2 +
J^2$ in the parameter space spanned by $h$, $\de$ and $\ga$. By mapping to an
equivalent two-level Landau-Zener problem, we show that the defect density in
the final state scales as $1/\tau^{1/3}$, a behavior that has not been observed
in previous studies of quenching through a gapless phase. We also generalize
the model incorporating additional alternations in the anisotropy or in the
strength of the interaction, and derive an identical result under a similar
quenching. Based on the above results, we propose a general scaling of the
defect density with the quenching rate $\tau$ for quenching along a gapless
critical line.
