The amplitude of a wave, represented by displacement equation $y=\frac{1}{\sqrt{a}} \sin \omega t \pm…

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
  1. $\frac{a+b}{a b}$
  2. $\frac{\sqrt{a}+\sqrt{b}}{a b}$
  3. $\frac{\sqrt{a} \pm \sqrt{b}}{a b}$
  4. $\sqrt{\frac{a+b}{a b}}$

Solution

The displacement equation presented by $\begin{aligned} & y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t \\ & =\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \sin \left(\omega t+\frac{\pi}{2}\right)\end{aligned}$ Here phase difference $=\frac{\pi}{2}$ The amplitude of wave, $A=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^2+\left(\frac{1}{\sqrt{b}}\right)^2}=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{a b}}$

Asked in: AP EAMCET 2023 (16 May Shift 1)

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