  The phenomenon of steady streaming, or acoustic streaming, is an important
physical phenomenon studied extensively in the literature. Its mathematical
formulation involves the Navier-Stokes equations, thus due to the complexity of
these equations is usually studied heuristically using formal perturbation
expansions. It turns out that the Burgers equation formulated on the half line
provides a simple model of the above phenomenon. The physical situation
corresponds to the solution of the Dirichlet problem on the half-line, which
decays as $x \to \infty$ and which is {\it time periodic}. We show that the
Dirichlet problem, where the usual prescription of the initial condition is now
replaced by the requirement of the time periodicity, yields a well posed
problem. Furthermore, we show that the solution of this problem tends to the
``inner'' and ``outer'' solutions obtained by the perturbation expansions.
