Equation of motion in the same direction is given by `y_1=Asin(omegat-kx)`, `y_2=Asin(omegat-kx-theta)`. The amplitude of the medium particle will be

Options

A. `2Acos"(theta)/(2)`
B. `2Acostheta`
C. `sqrt(2)Acos"(theta)/(2)`
D. `sqrt(2)Acostheta`

Answer

A

Explanation

`y=y_(1)+y_(2)`
`=Asin(omegat-kx)+Asin(omegat-kx-omega)`
`=A[sin(omegat-kx)+sin(omegat-kx-omegat)]`
`implies y=2Asin(omegat-kx-(theta)/(2))cos"(theta)/(2)`
`implies y=2Acos"(theta)/(2)sin(omegat-kx-(theta)/(2))`
Resultant amplitude
`A.=2Acos"(theta)/(2)`.