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A radio transmitting station operating at a frequency of 125 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?

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ajeigbeibraheem

Answer:

Explanation:

The formula for frequency is:

[tex]f = \dfrac{c}{\lambda}[/tex]

If we make [tex]\lambda[/tex] the subject; we have:

[tex]\lambda = \dfrac{c}{f}[/tex]

[tex]\lambda = \dfrac{3\times 10^6 \ m/s}{125 \ MHz (\dfrac{10^6 \ Hz}{1 \ MHz})}[/tex]

[tex]\lambda = 2.4 \ m[/tex]

Let assume that there is a point P between antenna A  to B.

where;

A to B = 9.05

A to P = x  and

P to B = 9.05 - x

Then, the condition for the constructive inteference is:

Δx = nλ

x - (9.05 - x) = nλ

2x - 9.05 = n(2.4)

So, we need to start assigning values to n so that the value of x becomes less than or equal to 9.05 m

If n = -1

Then;

2x - 9.05 = (-1)(2.4)

x = 3.325 m

If n = -2

Then;

2x - 9.05 = (-2)(2.4)

x = 2.125 m

If n = -3

Then;

2x - 9.05 = (-3)(2.4)

x = 0.925 m

If n = 0

Then;

2x - 9.05 = (0)(2.4)

x = 4.525 m

If n = 1

2x - 9.05 = (1)(2.4)

x = 5.725 m

If n = 2

Then;

2x - 9.05 = (2)(2.4)

x = 6.925 m

Hence, there exist 7 points in which constructive interference occurs.

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