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 th

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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.

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  1. 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 = 3×10⁸m/s

    f = 125 MHz = 125×10⁶Hz

    Replacing:

    [tex]\lambda =\frac{3×10^{8} }{125×10^{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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