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
$\frac{a+b}{a b}$
$\frac{\sqrt{a}+\sqrt{b}}{a b}$
$\frac{\sqrt{a} \pm \sqrt{b}}{a b}$
$\sqrt{\frac{a+b}{a b}}$
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,
$A=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^2+\left(\frac{1}{\sqrt{b}}\right)^2}=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{a b}}$