Two waves are represented by `y_(1)= a sin (omega t + ( pi)/(6)) and y_(2) = a cos omega t `. What will be their resultant amplitude

Options

A. `sqrt3A`
B. `sqrt2A`
C. 2A
D. A

Answer

A

Explanation

`y_(1) = A sin [omega t + (pi)/(6)], y_(2) = A sin [omega t + (pi)/(2)]`
`:.` Phase diff. `= (pi)/(2) - (pi)/(6) = (pi)/(3)`
`R = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1) A_(2) cos theta)`
But `A_(1) = A_(2) = A and theta = pi//3`
`:. R = sqrt(2A^(2) + 2A^(2) xx (1)/(2)) = sqrt(3A^(2)) = sqrt3A`