  The propagation of an external transverse magnetic signal acting locally on a
1d chain of spins generates a disturbance which runs through the system. This
quantum effect can be interpreted as a classical traveling wave which contains
a superposition of a large set of frequencies depending on the size of the
chain. Its local amplitude fixes the size of the z-component of the spins at
any location in the chain. The average and maximum value of the group velocity
are determined and compared with the transmission velocity fixed by the
Lieb-Robinson upper bound inequality.
