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

Assume `1//sqrt(a)=A cos theta`
`(1)/sqrt(b)=A sin theta`
On simplifying, we get `y=A sin(omegat+theta)`
squaring and adding Eqs. (i) and (ii) `A=sqrt((a+b)/(ab))`