Question

The equations of two waves given as $x=acos\ (ωt + δ)$ and $y=a cos\ (ωt+α)$, Where $δ=α+\frac \pi 2$, then resultant wave represent:

• A. a circle (c.w)
• B. a circle (a.c.w)
• C. an Ellipse (c.w)
• D. an ellipse (a.c.w)

Answer 1

Answer: (B)

a circle (a.c.w)

Answer 2

When two waves are given by:
$x = a cos\ (ωt + δ)$
$y = a cos\ (ωt + α)$
And it's given that $δ = α +\frac \pi2$, it means that the phase difference between the two waves is $\frac \pi2$.
The resultant wave can be represented by the vector sum of these two waves. If the phase difference between them is $\frac \pi2$, then the resultant will be a circularly polarized wave.

So, the correct answer is (B): a circle (a.c.w)