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
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d) $y = \frac{1}{{\sqrt a }}\sin \omega t \pm \frac{1}{{\sqrt b }}\sin \left( {\omega t + \frac{\pi }{2}} \right)$
Here phase difference =$\frac{\pi }{2}$
$\therefore $ 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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