d
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

= \(\sqrt {{{\left( {\frac{1}{{\sqrt a }}} \right)}^2} + {{\left( {\frac{1}{{\sqrt b }}} \right)}^2}} = \sqrt {\frac{1}{a} + \frac{1}{b}} = \sqrt {\frac{{a + b}}{{ab}}} \)