  We study relaxation of long-wavelength density perturbations in one
dimensional conserved Manna sandpile. Far from criticality where correlation
length $\xi$ is finite, relaxation of density profiles having wave numbers $k
\rightarrow 0$ is diffusive, with relaxation time $\tau_R \sim k^{-2}/D$ with
$D$ being the density-dependent bulk-diffusion coefficient. Near criticality
with $k \xi \gsim 1$, the bulk diffusivity diverges and the transport becomes
anomalous; accordingly, the relaxation time varies as $\tau_R \sim k^{-z}$,
with the dynamical exponent $z=2-(1-\beta)/\nu_{\perp} < 2$, where $\beta$ is
the critical order-parameter exponent and and $\nu_{\perp}$ is the critical
correlation-length exponent. Relaxation of initially localized density profiles
on infinite critical background exhibits a self-similar structure. In this
case, the asymptotic scaling form of the time-dependent density profile is
analytically calculated: we find that, at long times $t$, the width $\sigma$ of
the density perturbation grows anomalously, i.e., $\sigma \sim t^{w}$, with the
growth exponent $\omega=1/(1+\beta) > 1/2$. In all cases, theoretical
predictions are in reasonably good agreement with simulations.
