The equations of two waves acting in perpendicular directions are given as x = a cos( ω t + δ) and y = a cos( ω t + α), where δ = α + π/2, the resultant wave represents (a) a parabola (b) a circle (c) an ellipse (d) a straight line

Answer: (b). With δ = α + π/2: x = acos (ω t + α + π/2) = -asin (ω t + α). y = acos (ω t + α) x² + y² = a²: equal amplitudes with π/2 phase difference. So the answer is (b) a circle.

The equations of two waves acting in perpendicular directions are… | NEET 2000 (AIPMT)

Q39NEET 2000 · AIPMTEasy

Wave Basics & Properties of Sound

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

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Answer: (b)

With $\delta = \alpha + \frac{\pi}{2}$ : $x = a\cos(\omega t + \alpha + \frac{\pi}{2}) = -a\sin(\omega t + \alpha)$ .
$y = a\cos(\omega t + \alpha)$
$x^2 + y^2 = a^2$ : equal amplitudes with $\frac{\pi}{2}$ phase difference.
So the answer is (b) a circle.

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