A radio transmitting station operating at a frequency of 120MHz has two identical antennas that radiate in phase. Antenna B is 9.00m to the right of antenna A. Consider point P between the antennas and along the line connecting them, a horizontal distance x to the right of antenna A. For what values of x will constructive interference occur at point P?

Options

A. `x = 14.95 m, n = 1`
B. `x = 5.6 m, n = 2`
C. `x = 1.65 m, n = 3`
D. `x = 0 m, n = 3.6`

Answer

a.,b.,c

Explanation

Path difference, `delta = BP - AP`
`sqrt(x^(2) + 9^(2)) - x = n lambda`
`implies x^(2) + 9^(2) - n^(2) lambda^(2) + x^(2) + 2 n lambda x`
`implies x = (9^(2) - n^(2) lambda^(2))/(2 n lambda)`
`lambda = ( c) /(v) = (3 xx 10^(8))/(120 xx 10^(6)) = 2.5 m`
`n = 1, x = 14.95 m, n = 3, x = 1.6 m,`
`n = 2, x = 5.6 m, n = 4` not possible