WAVES OF MAGNETIC FLUX 39 



Wo now have 



y = P, sin /if . sin qx 



From tli is equation \ve see that while at every instant (i.e. for 

 every value of t) the magnetic flux is distributed in space according 

 to the sine law, and while the points of zero flux remain fixed, the 

 actual value of the flux at every point undergoes simple oscillations 

 according to the sine law. This means that the ordinates of the 

 curve in Fig. 28 oscillate about the base line. In Fig. 29 are 

 indicated the positions of the curve corresponding to equal time 

 intervals, each of which = ^T. Thus our wave of magnetic flux is 

 an oscillating wave whose zero points or nodes remain fixed ; such a 

 wave is frequently spoken of as a stationary wave. We may also 

 speak of it as a simple alternating wave of magnetic flux. 



19. Analysis of Alternating into Two Rotating 

 Waves, and vice versa 



The expression for y may be thrown into a slightly different form. 

 We have 



y = B sin pt . sin qx 

 = B . 2 sin pt . sin qx 

 = B{cos (pt qx) cos (pt + qx)} 

 = B cos (pt qx) B cos (pt + qx) 



From this we see that y may be split up into 



yi = B cos (pt qx) 

 and 



7/2 = - B cos (pt + qx) 



Let us consider the meanings of y\ and y 2 . If we assign to t any 

 definite value, then clearly both y\ and y 2 will represent a magnetic 

 flux distributed in the air-gap according to the simple sine (or cosine) 

 law. Taking the particular instant t = 0, we find 



and 



where the symbol [yi] t _ denotes the value of y\ at the instant t = 0. 

 The values of [yi] t = Q and [y%] t _ have been plotted in Fig. 30, and 

 are shown by the full-line curves. When t has increased to T, we 

 find 



