The amplitude of a wave represented by displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$ will be
$(a) \frac{a+b}{ab} (b) \frac{\sqrt{a}+\sqrt{b}}{ab} (c) \frac{\sqrt{a} \pm \sqrt{b}}{ab} (d) \sqrt{\frac{a+b}{ab}}$
Text Solution
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$y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \sin \left( \omega t + \frac{\pi}{2} \right)$
Here phase difference = $\frac{\pi}{2}$ $\begin{matrix} \bullet \\ \bullet & \bullet \end{matrix}$ The resultant amplitude
= $\sqrt{\left(\frac{1}{\sqrt{a}}\right)^2 + \left(\frac{1}{\sqrt{b}}\right)^2} = \sqrt{\frac{1}{a} + \frac{1}{b}} = \sqrt{\frac{a+b}{ab}}$
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