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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? Enter your answers in ascending order separated by a comma.

Answer :

Answer:

The answer is: 4.53 m, 4.03 m, 2.13 m, 0.93 m,..., are the values of x constructive interference occur at point P

Explanation:

The wavelength is:

[tex]\lambda =\frac{v}{f}[/tex]

Where

v = 3x10⁸m/s

f = 125 MHz = 125x10⁶Hz

Replacing:

[tex]\lambda =\frac{3x10^{8} }{125x10^{6} } =2.4m[/tex]

The expression of path difference is equal:

9.05 - x - x = 9.05 -2x (exp. 1)

nλ (exp. 2)

Matching both expressions:

9.05 - 2x = nλ

9.05 - 2x = 2.4λ

Integers for n between 0 and 9.05

For n = 0

[tex]9.05-2x=0*2.4\\9.05-2x=0\\2x=9.05\\x=\frac{9.05}{2} =4.53m[/tex]

For n = 1

[tex]9.05-2x=1*2.4\\9.05-2x=1\\2x=9.05-1\\x=\frac{8.05}{2} =4.03m[/tex]

For n = 2

[tex]9.05-2x=2*2.4\\9.05-2x=4.8\\2x=9.05-4.8\\x=\frac{4.25}{2} =2.13m[/tex]

For n = 3

[tex]9.05-2x=3*2.4\\9.05-2x=7.2\\2x=9.05-7.2\\x=\frac{1.85}{2} =0.93m[/tex]

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