SINE WAVES 5 



The maximum value Y of the sine wave is termed its amplitude. 

 A complete cycle of changes clearly corresponds to a complete 

 revolution of OP, or to the time T taken by OP to sweep out an 

 an^'lo of 2;r radians. Since the angular velocity is p, we have 



pT = 27r, or p = . We have already (1) termed T the period. 

 Now if the frequency or number of complete cycles per second be 

 denoted by n, we have T = -, so that p = 2irn ; i.e. the angular 



velocity of the rotating vector in the vector diagram is equal to 2ir times 

 the frequency. 



If the equation of the sine wave is given in the form 



yi = Y! sin (pt + 9) 



then yi may as before be represented by the projection on the vertical 

 of a rotating vector of length YI, the only difference now being that 

 at the time t = this rotating vector is not horizontal, but makes 

 an angle + with the horizontal. 



Since the rotating vectors from which y and y\ are derived have 



Fio. 4. Graphs of Two Sine Waves, with a Phase Difference 0. 



the same angular velocity p, the angle between them must remain 

 constant and equal to 9, which is the angle they make with each 

 other at the time t = 0. This constant angle 6 is the phase difference 

 between the two sine waves y and y\. The wave y is said to lag 

 behind y\, and y\ is said to lead with respect to y, the angle being 



