Appendix C.l 



The addition of two sinusoids of different amplitude and phase, but 

 identical wavelength results in another sinusoid of the same wavelength, 

 but amplitude and phase which is a function of the amplitudes and phases 

 of the component sinusoids. Assuming two sinusoids of differing ampli- 

 tudes (v. and Vg) and phases (9^ and 9g), their sum can be expressed in 

 terras of a new sinusoid of amplitude Vq and phase ^(^ as 



v^ • cos(e-e^) + vg • cos(e-9g) = v^, • cos(e-9(,) (c-i) 



Using the addition formula of sinusoids, 



v. • cos9 • cos9^ + v^ • 3ln9 • sin9^ + Vg • cos9 • cos9g + 



Vg • sin9 • 3in9g = v^, • cos9 • cos9^ + v^ • sin9 • sin9(, (C-2) 



Combining terras, and equating sine and cosine terras 



(v. • cos9 + Vg • cos9g) • cose = (v^ • cos9-) • cose (C-3) 



and 



(v^ • 3in9^ + Vg • sin9g) • sin9 = (V(, • sine^,) • sine (C-4) 



Since C-3 and C-4 are true for any value of 9, the unknown v^, and 9^ 

 are determined from: 



178 



