  Recent experiments on particle diffusion in bacterial baths indicate the
formation of correlated structures in the form of bacterial swirls. Here we
predict that such a structural ordering would give rise to the new effect of
propagating shear waves in a bacterial bath at length scales of the order of a
swirl, which corresponds to time scales of the order of the lifetime of a
swirl. Our prediction can be tested against future experiments in bacterial
baths.
