Question

The equations of two waves acting in perpendicular direction are given as $x=a\cos (\omega t+\delta )$ and $y=a\cos (\omega t+\alpha )$, where $\delta =\alpha +\frac{\pi }{2}$, the resultant wave represents

• A. a parabola
• B. a circle
• C. an ellipse
• D. a straight line

Answer 1

The correct option is B a circle

Given:
$x=a\cos (\omega t+\delta )$
and $y=a\cos (\omega t+\alpha )....\left(1\right)$
where, $\delta =\alpha +\frac{\pi }{2}$
$\therefore x=a\cos (\omega t+\frac{\pi }{2}+\alpha )=-a\sin (\omega t+\alpha )....\left(2\right)$
From Eqs. $\left(1\right)$ and $\left(2\right)$,
$x^2+y^2=a^2,$
which represents the equation of a circle.
Hence, the correct answer is option (b).