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A radio transmitting station operating a...

A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that radiate in phase. Antenna B is 9 m to the right of antenna A. consider point P at a horizontal distance x to the right of antenna A as shown in figure. The value of x and order for which the constructive interference will occur at point P are

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`

Text Solution

Verified by Experts

The correct Answer is:
a.,b.,c
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
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