It is not uncommon in nature for waves of different wavelength to have
different speeds. Light waves in transparent media have slightly different
wavelength dependent speeds, which leads to dispersion into the spectrum by
prisms.

The derivation of the dispersion relationship for gravitational surface
waves on fluids is somewhat complex and not obvious. It is found in many
fairly advanced mechanics texts. You will need to go to a college or
university library to find it. The result: wave speed is 1.3 times sq rt of
wavelength, where the 1.3 is a combination of the gravitational constant and
water density.

Brent
www.bensonsails.com

From: (Sakari Aaltonen)
Organization: Helsinki University of Technology
Newsgroups: rec.boats.building
Date: 16 Jul 2003 05:54:55 GMT
Subject: Hull speed theory?

I have seen lots and lots of references to the formula "X times
square root of waterline length" as defining hull speed with X
normally about 1.3 (speed in knots, length in Imperial feet.)
However, I have never seen an explanation of this.

Pictures of boats "trapped" between their bow and stern waves seem
to make sense. But they do not explain why a long wave would travel
faster than a short one.

Surely there is a book with the theory?


Thank you,
Sakari Aaltonen