WAVES 211 



The preceding diagrams represent these movements and the 

 resultant waves. (Fig. 32.) They show clearly the relation be- 

 tween the wave height and amplitude of the orbits, and that, with 

 the same wave length, the increase in the size of the orbit brings 

 about a corresponding increase in the height of the wave. At the 

 same time it will be noted that the crest becomes sharper, the slopes 

 being steeper and the angle more acute. If the velocity of the 

 moving particle remains the same with an increase in the size of the 

 orbit, the period must lengthen, because the particles have a longer 

 path to travel before they return to their starting point. If, on the 

 other hand, the period remains the same, or is shortened, giving 

 the same or greater velocity for the wave progress, the orbital 

 velocity of the particles must increase. This is also true when the 

 wave increases in height by an increase in the size of the orbit, as 

 is the case near shore. With the same size of orbit an increase in 

 the wave length brings about a reduction in the sharpness of the 

 crest. The change in wave length is brought about by a relative 

 change in the spacing of particles whose position in the orbit differs 

 by a uniform degree. Thus if, as in Fig. 32b. we have particles 

 selected from the wave surface revolving in immediately adjoining 

 orbits, of the size indicated and spaced so that they are just 45° 

 apart, we have the wave length AB, and the form given in the 

 dotted line. This means that the velocity of the wind is such that it 

 not only produces the orbit shown, but also reaches and sets in 

 motion the second particle at the moment the first particle has com- 

 pleted ys of its revolution. If, now, the velocity of the wind in- 

 creases, so that, when it reaches the next particle, the first one has 

 completed only 1/16 of its revolution, the wave length with the 

 same size orbit would become twice as great and correspondingly 

 flatter. But increased velocity of wind means an increase in the 

 size of the orbit, which in turn means an increase in the height of 

 the wave, and a sharpening of the crest. As the wave length in- 

 creases the period would lengthen correspondingly, since the dis- 

 tance to travel increases, unless the wave velocity also increases, 

 which means a great augmentation of the orbital velocity of the 

 moving particles. The period does increase in length, but not in 

 proportion to the increase in wave length. (See formula i, page 

 212.) Thus a wave with a length of 500 feet may have a period 

 of 10 seconds, which corresponds to a wave velocity of about 34 

 miles per hour. On increasing to 1,500 feet, the period will increase 

 to between 17 and 18 seconds, corresponding to a wave velocity of 

 about 56 miles per hour. If the wave velocity had remained the 

 same, the period would have been 30 seconds. The disproportional 



