Two particles `P` and `Q` describe `S.H.M.` of same amplitude a, same frequency `f` along the same straight line from the same mean position. The maximum distance between the two particles is a `sqrt(2)`, If the initial phase difference between the particles is `(pi)/(N)` then find `N` :

Options

A. zero
B. 2
C. 6
D. 3

Answer

B

Explanation

`x_(1) = a sin( omega t + phi_(1))`
`x_(2) = a sin(omega t + phi_(2))`
`rArr |x_(1) - x_(2)| = 2a sin( sin + (phi_(1) + phi_(2))/(2)) cos ((phi_(1) - phi_(2))/(2))`
To maximize: `|x_(1) - x_(2)|sin (omegat + (phi_(1) + phi_(2))/(2)) cos (phi_(1) - phi_(2)) = 1`
`rArr asqrt(2) = 2a xx 1 xx cos ((phi_(1) - phi_(2))/(2))`
`rArr (1)/(sqrt(2)) = cos ((phi_(1) - phi_(2))/(2))`
`rArr (pi)/(4) = (phi_(1) - phi_(2) rArr phi_(1) - phi_(2)= (pi)/(2)`