  We consider the propagation of acoustic, electromagnetic and elastic waves in
a one-dimensional periodic two-component material. Accurate asymptotic formulas
are provided for the group velocity as a function of the material parameters
when the concentration of scatterers is small or the characteristic impedances
of the two media differ substantially. In the latter case, it is shown that the
minimum group velocity occurs when the volume fractions of the components of
the material are equal. In both asymptotic cases we show that the leading terms
of the group velocity do not depend on frequency. Thus slowdown is
frequency-independent and is not related to the resonance phenomena.
