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Water Waves

Although all sorts of waves are ubiquitous in our lives,^14.9 our most familiar ``wave experiences'' are probably with water waves, which are unfortunately one of the least simple types of waves. Therefore, although water waves are routinely used for illustration, they are rarely discussed in great depth (heh, heh) in introductory Physics texts. They do, however, serve to illustrate one important feature of waves, namely that not all waves obey the simple relationship   $c = \omega/k$  for their propagation velocity  c.

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.