The equations of two waves acting in perpendi | vedclass

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(A) Given equations are $x=a \cos (\omega t+\delta)$ and $y=a \cos (\omega t+\alpha)$.Substituting $\delta=\alpha+\frac{\pi}{2}$ into the equation for

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a circle $(c.w)$

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(A) Given equations are $x=a \cos (\omega t+\delta)$ and $y=a \cos (\omega t+\alpha)$.Substituting $\delta=\alpha+\frac{\pi}{2}$ into the equation for $x$:$x=a \cos (\omega t+\alpha+\frac{\pi}{2}) = -a \sin (\omega t+\alpha)$.Now,squaring and adding both equations:$x^2+y^2 = (-a \sin (\omega t+\alpha))^2 + (a \cos (\omega t+\alpha))^2 = a^2 (\sin^2 (\omega t+\alpha) + \cos^2 (\omega t+\alpha)) = a^2$.This is the equation of a circle with radius $a$.To determine the direction,at $t=0$,$x = -a \sin \alpha$ and $y = a \cos \alpha$. As $t$ increases,the point moves in the clockwise $(c.w)$ direction.

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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