Two particles execute SHM of same amplitude and frequency on parallel lines. They pass one another when moving in opposite directions each time their displacement is one third their amplitude. What is the phase difference between them?

Options

A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(6)`
D. `(2 pi)/(3)`

Answer

D

Explanation

Equation of simple harmonic wave, `y = A sin (omega t + phi)`
Here, `y = (A)/(2)`
`therefore" "A sin (omega t + phi)=(A)/(2)`
`rArr" "delta = omega t + phi = (pi)/(6) or (5 pi)/(6)`
So, the phase difference of the two particles when they are crossing each other at `y = (A)/(2)` in opposite directions are
`delta=delta_(1)-delta_(2)=(5pi)/(6)-(pi)/(6)=(2pi)/(3)`