A radio transmitter at position `A` operates at a wavelength of `20 m`. A second , identical transmitter is located at a distance `x` from the first transmitter , at position `B`. The transmitters are phase locked together such that the second transmitter is lagging `pi//2` out of phase with the first . For which of the following values of `BC - CA` will the intensity at `C` be maximum .

Options

A. `BC - CA = 60 m`
B. `BC - CA = 65 m`
C. `BC - CA = 55 m`
D. `BC - CA = 75 m`

Answer

C, D

Explanation

`y_(A) = A sin [ omega t - k (AC)]`
`y_(B) = sin [ omega t - (pi)/(2) - k (BC)]`
For maximum intensity at `C`
`k (BC - AC) + (pi)/(2) = 2 n pi`
`BC - AC = ( n lambda - (lambda)/(4)) = 15 , 35 , 55 , 75 ,….`