Question

Two radius antennas radiating wave in phase are located at point `A` and `B` ,`200m` part(figure) The radio waves have a frequency of `6MHz`.A radio receiver in moved out form point`B` along a line perpendicular to the line connecting `A` and `B`(line`BC` shown in figure)at time distances from `B` will there be destructive interference?

Answer 1

Correct Answer - `787,5m,229m,97.5m,26.7m`

`C=nlambda rArr lambda=(C )/(n)`
`lambda=(3xx10^(8))/(6xx10^(6))rArr lambda=50m`
path difference at P=AP-BP
path difference at P=`sqrt((4lambda)^(2)+x^(2))-x`
For districtive interference at P
path difference=`(2n-1)(lambda)/(2)....(2)`
From (1)&(2)
`sqrt((4lambda)^(2)+x^(2))-x=(2n-1)(lambda)/(2)`
`sqrt((4lambda)^(2)+x^(2))=(2n-1)(lambda)/(2)+x`
For first minima `n=1,x_(1)=(63lambda)/(4) rArr x_(1)=787.5m`
For second minima `n=2,n_(2)=(55lambda)/(2) rArr x_(2)=229m`
For third minima `n=3,n_(2)=(39lambda)/(20)rArr x_(3)=92.5m`