miscellaneous: Practice Problem & Solution
The equations of two waves given as $x = a\cos(\omega t + \delta)$ and $y = a\cos(\omega t + \alpha)$, Where $\delta = \alpha + \pi/2$, then resultant wave represent: (2000)
Solution Explained:
To solve this problem, we apply the core principles of miscellaneous. Understanding the underlying formula is key to arriving at the correct answer below:
Substitute $\delta$: $x = a\cos(\omega t + \alpha + \pi/2) = -a\sin(\omega t + \alpha)$.\nCombining with $y = a\cos(\omega t + \alpha)$ yields $x^2 + y^2 = a^2$, a circle.\nThe direction of motion traces anti-clockwise as time progresses.
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