Question

The amplitude of a wave represented by displacement equation y=1/sqa

Answer 1

consider it as 2 vector

one is \frac{1}{\sqrt{a}}sin\omega t with amplitude \frac{1}{\sqrt{a}}

another is perpendicular to it \frac{1}{\sqrt{b}}cos\omega t with amplitude \frac{1}{\sqrt{b}}

and amplitude of the resultant of two perpendicular vector is given as  

\sqrt{\frac{1}{\sqrt{a}^2} +\frac{1}{\sqrt{b}^2} }