Let's restrict ourselves to deep ocean waves, where the "restoring force" is simply gravity. (When a wave reaches shallow water, the bottom provides an immobile boundary that complicates matters severely, as anyone knows who has ever watched surf breaking on a beach!) The motion of an "element" of water in such a wave is not simply "up and down" as we pretended at the beginning of this chapter, but a superposition of "up and down" with "back and forth" in the direction of wave propagation. A cork floating on the surface of such a wave executes circular motion, or so I am told. (It is actually quite difficult to confirm this assertion experimentally since it requires a fixed reference that is not moving with the water - a hard thing to arrange in practice without disturbing the wave itself.) More importantly, the propagation velocity of such waves is higher for longer wavelength.