Find the resultant amplitude and phase of a point at which N sinusoidal waves interfere. All the waves have same amplitude A and their phases increase in arithmetic progression of common difference phi.

Find the resultant amplitude and phase of a point at which N sinusoida

1.	Find the resultant amplitude and phase of a point at which N sinusoidal waves interfere. All the waves have same amplitude A and their phases increase in arithmetic progression of common difference phi.
Answer» SOLUTION :The diagram for their SUM is shown in figure for N=6. The resultant amplitudes is `A_(R)`. The apex angle of every ISOSCELES TRIANGLE is `phi`. So, the angle subtended by the resultant is `Nphi`. Since, the heads of the vectors are all at the same distance r from the apex of the diagram. From Fig. (a), `A_(R)/2 = r sin (Nphi)/2 ` and from Fig. (b), `A/2 = r sin (phi/2)` DividingEq. (i) by Eq. (II), we get `A_R/A = (sin(Nphi)/2)/("sin"(phi)/(2))` `A_(R) = A ((sin((Nphi)/2))/(sin(phi/2)))`s