The amplitude of a wave represented by displacement equation `y=(1)/(sqrta)sinomega+-(1)/(sqrtb)cosomegat` will be

Options

A. `(a+b)/(ab)`
B. `(sqrta+sqrtb)/(ab)`
C. `(sqrta+-sqrtb)/(ab)`
D. `sqrt((a+b)/(ab))`

Answer

D

Explanation

`y=(1)/(sqrta)sinomegat+-(1)/(sqrtb)sin(omegat+(pi)/(2))`
Here phase difference `=(pi)/(2)`
Resultant amp.`=sqrt(((1)/(sqrta))^2+((1)/(sqrtb)^2))=sqrt((1)/(a)+(1)/(b))=sqrt((a+b)/(ab))`