Two particles A and B have a phase diference of `pi` when a sine wave passes through the regin

Options

A. `A` oscillates at half the frequency of `B`
B. `A` and `B` move in opposite direction
C. `A` and `B` must be separted by half of the wavelength
D. the displacement of `A` and `B` have equal magnitudes

Answer

b., c., d.

Explanation

`(Deltaphi)/(2pi)=(Deltax)/(lambda)`
`Deltax=(lambda)/(2pi)Deltaphi`
`=(lambda)/(2pi)pi=(lambda)/(2)`
let for P: `y_(1)=A sin omega t`, then
For Q: n`y_(2)=A sin(omega t-pi)=-A sin omega t`
we see that `y_(1)=-y_(2)`
and `|y_(1)|=|y_(2)|`
Frequency of both particle should be same because the same wave passes through them.