When we use the expression, a long wave, we do not mean a wave which is of great length in the direction of the ridge, but waves in which the crests, or humps, are separated far apart, measuring from crest to crest across the ridges.
Strictly speaking, the wave-length may be defined as the shortest distance from crest to crest, or hollow to hollow, or from one particle to the next one which is in the same stage of its movement at the same time.
Another way of illustrating the same thing would be to pleat or pucker a sheet of paper into parallel ridges. If we make these pleats very narrow, they would represent what we call short waves; but if we make these pleats very far apart, they would represent long waves.
Another phrase much used is the term wave-velocity. Suppose that a seagull were to fly along over a set of sea waves so as to keep always above one particular hump, or wave-crest; the speed of the gull, reckoned in miles per hour or feet per minute, would be called the speed of the waves. This is something very different from the actual speed of each particle of water.
A third and constantly used expression is the term wave-frequency. If we watch a cork floating on a wave-tossed sea, we observe that it bobs up and down so many times in a minute. The number of times per second or per minute that each particle of the medium performs its cycle of motion is called the wave-frequency, or simply the frequency.
Again, we employ the term amplitude to denote the extreme distance that each individual particle of the medium moves from its mean position, or position of rest. In speaking of sea waves, we generally call the vertical distance between the crest and the hollow the height of the wave, and this is twice the amplitude. With regard to the height of sea waves, there is generally much exaggeration. Voyagers are in the habit of speaking of “waves running mountains high,” yet a sea wave which exceeds 40 feet in height is a rare sight. Waves have been measured on the Southern Indian Ocean, between the Cape of Good Hope and the Island of St. Paul, and of thirty waves observed the average height was found to be just under 30 feet. The highest was only 37¹⁄₂ feet in height. On the other hand, waves of 16 to 20 feet are not uncommon. Travellers who have crossed the Atlantic Ocean in stormy weather will often recount experiences of waves said to be 100 feet high; but these are exceedingly rare, if even ever met with, and unless wave-heights are obtained by some accurate method of measurement, the eye of the inexperienced voyager is apt to be deceived.
In all cases of wave-motion there is a very close connection between the wave-velocity, or speed, the wave-length, and the wave-frequency. This connection is expressed by the numerical law that the velocity is equal to the product of the length and the frequency.
Thus, supposing we consider the case of Atlantic waves 300 feet from crest to crest, which are travelling at the rate of 27 miles an hour, it is required to calculate the frequency or number of times per minute or per second that any floating object, say a boat, will be lifted up as these waves pass over it.
We must first transform a speed of 27 miles per hour into its equivalent in feet per second. Since one mile is 5280 feet, 27 miles per hour is equal to 2376 feet per minute. Accordingly, it is easy to see that the wave-frequency must be 7·92, or nearly 8, because 7·92 times 300 is 2376. The answer to the question is, then, that the floating object will rise and fall eight times a minute. This rule may be embodied in a compact form, which it is desirable to hold firmly in the memory, viz.—
Wave-velocity = wave-length × wave-frequency.