SPECTRUM ANALYSIS OF WAVES 387 



For the J-c term, 



, EAL £, . , 



9 T' "^ ? sin vt. 



For the fundamental or c term, 



2E /tt . \ 



Ai cos ItcI = — ■ cos KT^k sin z;^ ) cos Iwcl 



Using the Bessel's expansion of cos (2 sin 6), we get, 



\Jo{k) cos 27rc 



_g +/2(^) cos 27r(c — 2v)t 

 Ai cos 27rc/ = -— 



-^ +/-2(/^) COS 27r(c + 2v)t 



[-] etc. 



In a similar fashion, the other terms can also be computed, giving the 

 spectrum shown on Fig. 12, where Joik) becomes the amplitude of c, J2{k) 

 the amplitude of either c -{- 2votc — 2v, etc. 



