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Waves question

2000 · Q163
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Waves question

2000 · Q163

NEETPhysicsWavesMCQ+4 / −1
The equations of two waves acting in perpendicular directions are given as
x = aaacos(ω\omegaωt +δ\deltaδ) and y = aaacos(ω\omegaωt + α\alphaα), where δ\deltaδ = α\alphaα + π2{\pi \over 2}2π​, the resultant wave represents
  1. A
    a parabola
  2. B
    a circle
  3. C
    an ellipse
  4. D
    a straight line
View written solutionFree

Correct answer: B

Given : x = acos(ω\omega ωt + δ\delta δ)
and y = acos(ω\omega ωt + α\alpha α)     ...(i)

where, δ=α+π/2\delta = \alpha + \pi /2δ=α+π/2

∴x=acos(ωt+α+π/2) \therefore {\rm{x = acos(}}\omega {\rm{t + }}\alpha {\rm{ + }}\pi {\rm{/2)}}∴x=acos(ωt+α+π/2)

= –asin(ω\omega ωt + α\alpha α) ...(ii)

Given the two waves are acting in perpendicular direction with the same frequency and phase difference π\pi π/2.

From equations (i) and (ii),
x2 + y2 = a2
which represents the equation of a circle.

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