Question

The equations of two waves acting in perpendicular directions 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 circle (c.w)
• B. a circle (a.c.w)
• C. an Ellipse (c.w)
• D. an ellipse (a.c.w)

Answer 1

Answer: (B)

Given : $x = a \cos(\omega t+\delta)$
and $y= a \cos (\omega t+ \alpha)...(i)$
where, $\delta=\alpha+\pi/2$
$\therefore x=a \cos(\omega t+\alpha+\pi/2)$
$=- a \sin (\omega t+\alpha) ...(ii)$
Given the two waves are acting in perpendicular direction with the same frequency and phase difference $\pi/2$
From equations (i) and (ii),
$x^2 + y^2 = a^2$
which represents the equation of a circle.