  We experimentally and theoretically investigate the anisotropic speed of
sound of an atomic superfluid (SF) Bose-Einstein condensate in a 1D optical
lattice. Because the speed of sound derives from the SF density, this implies
that the SF density is itself anisotropic. We find that the speed of sound is
decreased by the optical lattice, and the SF density is concomitantly reduced.
This reduction is accompanied by the appearance of a normal fluid in the purely
Bose condensed phase. The reduction in SF density -- first predicted [A. J.
Leggett, Phys. Rev. Lett. 1543--1546 (1970)] in the context of supersolidity --
results from the coexistence of superfluidity and density modulations, but is
agnostic about the origin of the modulations. We additionally measure the
moment of inertia of the system in a scissors mode experiment, demonstrating
the existence of rotational flow. As such we shed light on some supersolid
properties using imposed, rather than spontaneously formed, density-order.
