  The realization that forthcoming experimental studies, such as the ones
planned for the GLAST space telescope, will be sensitive to Planck-scale
deviations from Lorentz symmetry has increased interest in noncommutative
spacetimes in which this type of effects is expected. We focus here on
$\kappa$-Minkowski spacetime, a much-studied example of Lie-algebra
noncommutative spacetime, but our analysis appears to be applicable to a more
general class of noncommutative spacetimes. A technical controversy which has
significant implications for experimental testability is the one concerning the
$\kappa$-Minkowski relation between group velocity and momentum. A large
majority of studies adopted the relation $v = dE(p)/dp$, where $E(p)$ is the
$\kappa$-Minkowski dispersion relation, but recently some authors advocated
alternative formulas. While in these previous studies the relation between
group velocity and momentum was introduced through ad hoc formulas, we rely on
a direct analysis of wave propagation in $\kappa$-Minkowski. Our results lead
conclusively to the relation $v = dE(p)/dp$. We also show that the previous
proposals of alternative velocity/momentum relations implicitly relied on an
inconsistent implementation of functional calculus on $\kappa$-Minkowski and/or
on an inconsistent description of spacetime translations.
