Designating this distance by 'z', the orbit radii are given by

where a is the wave amplitude (as shown).

So, if we know the wave's length and amplitude, we should be able to use Equation 1 to determine how deep we can 'feel' a surface disturbance.

The wave period is simply the time between consecutive wave crests as they pass a fixed point. All deep-water waves with the same period, regardless of actual depth, have the same wave length.

Let's see what happens for 2-foot waves (a=1 foot) with various periods. In particular, let's see how deep you must go before the orbit radii of small bits of floating debris become smaller than 1 inch, which implies an overall particle displacement of less than 2 inches. The results are presented in the following table.

For example, 2 foot waves 3 seconds apart produce a 2-inch particle displacent at 23 feet below the surface. As is clear from Equation 1, the longer the wave length the less rapid the vertical attenuation of the surface disturbances.

*Robert M. Sorensen, "Basic Wave Mechanics for Coastal and Ocean Engineers" (John Wiley & Sons, 1993), Chapter 2..*