  We consider pattern formation in periodically forced binary systems. In
particular we focus on systems in which the two species are differentially
forced, one being accelerated with respect to the other. Using a continuum
model consisting of two isothermal ideal gases which interact via a frictional
force we demonstrate analytically that stripes form spontaneously above a
critical forcing amplitude. The wavelength of the stripes is found to be close
to the wavelength of sound in the limit of small viscosity. The results are
confirmed numerically. We suggest that the same mechanism may contribute to the
formation of stripes in experiments on horizontally oscillated granular
mixtures.
