Correct question:
A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that radiate in phase. Antenna B is 9.05 m 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?
Answer:
values of x in which constructive interference will occur at point P are; 0.775 m, 2.025 m, 3.275 m, 4.525 m, 5.775 m, 7.025 m, 8.275 m
Explanation:
Given;
frequency, F = 120 MH = 120 x 10⁶ Hz
distance between A and B = 9.05 m
make a sketch of this antenna
A-------------------P------------------B
x 9.05 - x
Now, we calculate the wavefront between the two antenna
λ = v/f
where;
v is speed of light = 3 x 10⁸ m/s
λ = (3 x 10⁸) / (120 x 10⁶)
λ = 2.5 m
Thus, the constructive interference = n(2.5)
For constructive interference to occur at point P, then
the path difference = constructive interference
Path difference = 9.05 - x - x
= 9.05 -2x
∴ 9.05 - 2x = n(2.5)
2x = 9.05 - n(2.5)
x = 4.525 - n(1.25)
Finally, determine the value of x for which n = -1, -2, -3 and 0, 1, 2, 3
when n = -1
x = 4.525 + 1(1.25)
x = 5.775m
when n = -2
x = 4.525 + 2(1.25)
x = 7.025m
when n = -3
x = 4.525 + 3(1.25)
x = 8.275m
when n = 0
x = 4.525 - 0(1.25)
x = 4.525m
when n = 1
x = 4.525 - 1(1.25)
x = 3.275m
when n = 2
x = 4.525 - 2(1.25)
x = 2.025m
when n = 3
x = 4.525 - 3(1.25)
x = 0.775m
Thus, values of x in which constructive interference will occur at point P are; 0.775 m, 2.025 m, 3.275 m, 4.525 m, 5.775 m, 7.025 m, 8.275 m
