Two radio antennas radiating waves in phase are located at points A and B, 200   m apart (Figure). The radio waves have a frequency of 6   MHz . A radio receiver is moved out from point B along a line perpendicular to the line connecting A and B (line BC as shown in the figure). At what distances from B will there be destructive interference?

Step-by-step solution

C = n λ ⇒ λ = C n λ = 3 × 10 8 6 × 10 6 ⇒ λ = 50m path difference at P = AP - BP path difference at P = 4 λ 2 + x 2 - x ..............(1) For destructive interference at P path difference = (2n -1) λ 2 ...............(2) From (1) and (2) 4 λ 2 + x 2 - x = 2n - 1 λ 2 4 λ 2 + x 2 = 2n - 1 λ 2 + x For first minima n = 1, x 1 = 6 3 λ 4 ⇒ x 1 = 787.5 m For second minima n = 2, x 2 = 5 5 λ 1 2 ⇒ x 2 = 2 2 9 m For third minima n = 3, x 3 = 3 9 λ 2 0 ⇒ x 3 = 9 7 . 5 m