  We calculate the ultrasonic attenuation in magnetic fields for
superconducting states with line nodes vertical or horizontal relative to the
RuO_2 planes. This theory, which is valid for fields near Hc2 and not too low
temperatures, takes into account the effects of supercurrent flow and Andreev
scattering by the Abrikosov vortex lattice. For rotating in-plane field
H(theta) the attenuation alpha(theta)exhibits variations of fourfold symmetry
in the rotation angle theta. In the case of vertical nodes, the transverse T100
sound mode yields the weakest(linear)H and T dependence of alpha, while the
longitudinal L100 mode yields a stronger (quadratic) H and T dependence. This
is in strong contrast to the case of horizontal line nodes where alpha is the
same for the T100 and L100 modes (apart from a shift of pi/4 in field
direction) and is roughly a quadratic function of H and T. Thus we conclude
that measurements of alpha in in-plane magnetic fields for different in-plane
sound modes may be an important tool for probing the nodal structure of the gap
in Sr_2RuO_4.
