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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
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 $(c.w)$
  • ✓
    a circle $(a.c.w)$
  • C
    an Ellipse $(c.w)$
  • D
    an ellipse $(a.c.w)$
✓

Answer

Correct option: B.
a circle $(a.c.w)$
b
$x=a \cos (\omega t+\delta)$ and

$y=a \cos (\omega t+\alpha)$

$\delta=\alpha+\pi / 2$

$x=a \cos (\omega t+\alpha+\pi / 2)$

$x=-a \sin (\omega t+\alpha)$

$x^{2}+y^{2}=a^{2}$

which represents the equation of a circle.

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