Equation of motion in the same direction is given by `y_(1) =A sin (omega t - kx), y_(2) = A sin ( omega t - kx- theta )`. The amplitude of the medium particle will be

Options

A. `2A cos theta`
B. `1.2f, 1.2 lamda`
C. `sqrt2 A "cos"(theta)/(2)`
D. `2A "cos"(theta)/(2)`

Answer

D

Explanation

Resultant amplitude `A_(R)^(2) = A_(1)^(2) + A_(2)^(2) + 2A_(1) A_(2) cos theta`
`:. A_(R) = sqrt(A^(2) + A^(2) + 2A^(2) cos theta) :' A_(1) = A_(2) = A`
`= sqrt(2A^(2) (1 + cos theta)) = sqrt(2A^(2) xx 2 "cos"^(2) (theta)/(2))`
`:. A_(R) = 2A "cos" (theta)/(2)`