VELOCITY AND PERIOD 



35 



principle that large waves run with velocities not very different from 

 those of winds that produce them. But this is not a safe rule for 

 reasons stated previously, and because the effective fetch within storms 

 of this sort usually is not great enough for the waves produced there 

 to grow to the maximum dimensions theoretically possible for the 

 winds of such high velocities. For example, a wind of only 60 knots 

 (and hurricane winds often blow from 80 to 100 knots) requires a 

 fetch of something like 1,300 to 1,400 miles to produce waves long 

 enough to be advancing at velocities of 50 knots. 



Since the period, length, and velocity of a wave are interrelated, 

 the velocities of waves can be calculated from their periods, wherever 

 it happens to be easier to record the period than the length, the working 

 rule being that multiplication of the period in seconds by 3 gives the 

 velocity in knots. 12 A large number of calculations of this sort have 

 been made in many parts of the world, both for storm waves measured 

 on shipboard and for surf breaking on the shore. At first sight, the 

 rule that waves moving at the highest velocities have the longest 

 periods might seem contradictory to everyday experience. The reason 

 it applies is that a wave travelling at high velocity is so much longer 

 from crest to crest than is a wave of lower velocity that it occupies 

 a longer period of time in passing any given point. 



Measurements of the periods of waves can likewise be converted 

 into terms of length (since length is the feature of a wave that chiefly 

 governs its velocity) according to the formula that length, in feet, 

 is equal to the square of the period of the wave, in seconds, multiplied 

 by the factor 5.12. 



The relationship between the lengths and velocities of waves and 

 their periods is summarized in table 16, and in figure 5. 



Table 16. — Theoretical values of velocity (to nearest knot) and length (to nearest 

 foot) for waves of different periods in deep water 



Period (seconds) 



2. 

 4. 



f> 

 8_ 

 10 

 12 



Period (seconds) 



Velocity 

 (knots) 



14 

 16 



IN 



20 

 22 

 24 



Length 



(feet) 



1.004 

 1,311 

 1,659 

 2.048 



2. 47N 

 2. 940 



The theoretical values given in table 16, and presented in graphical 

 form in figure 5, agree quite closely with the relationship that has 

 been observed at sea, in different parts of the ocean, as illustrated in 

 table 17. The agreement between the theoretical and the observed 

 values is in fact good enough to show that, for this relationship, the 



n Actually the equation is C=3.037' where C=the velocity of the wave in knots, and T 

 its period, in seconds. This is a simplification of the formula given on page 32. 



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