  We present and analyze a multigrid algorithm for the acoustic single layer
equation in two dimensions. The boundary element formulation of the equation is
based on piecewise constant test functions and we make use of a weak inner
product in the multigrid scheme as proposed in \cite{BLP94}. A full error
analysis of the algorithm is presented. We also conduct a numerical study of
the effect of the weak inner product on the oscillatory behavior of the
eigenfunctions for the Laplace single layer operator.
