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Homework Help: Two antenas (two waves wih the same frequency)

  1. Mar 26, 2010 #1
    i really have some proplem with this question

    Two antennas located at points A and B are broadcasting radio waves of frequency 95.0 MHz, perfectly in phase with each other. The two antennas are separated by a distance d= 9.30 m. An observer, P, is located on the x axis, a distance x= 60.0 m from antenna A, so that APB forms a right triangle with PB as hypotenuse. What is the phase difference between the waves arriving at P from antennas A and B?

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    You are correct. Computer's answer now shown above.
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    Now observer P walks along the x axis toward antenna A. What is P's distance from A when he first observes fully destructive interference between the two waves?

    If observer P continues walking until he reaches antenna A, at how many places along the x axis (including the place you found in the previous problem) will he detect minima in the radio signal, due to destructive interference?

    i calculated the phase difference between the two antenas but i didnt know how to to calculate the first time that i will recieve a destructive interfernce i think that it is when the phase difference is pi*(2m+1)

    this is how i calculted the first quesion first i calculated the distance BP which is 60.716m
    then i used the equation (phase difference=2*pi*delta L/ג ) delta L=BP-AP and ג=c/frequency which is given
     
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  3. Mar 27, 2010 #2

    rl.bhat

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    You have already found ΔL. If at the point P instructive interference takes place, then
    ΔL = (2n + 1)*λ/2. ........(1)
    Find the wavelength.
    Substitute the value of the wavelength in eq(1) and find n. If n is not an integer, at P there is no destructive interference. Select the nearest integer less than n. That is the first point of destructive interference with in 60 m.
     
  4. Mar 27, 2010 #3
    hi
    I tried to do what you told me but it does not help when i calculated n its negative and after i calculate n how can I calculate the distance AP I attached my try to solve the proplem
     

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  5. Mar 27, 2010 #4

    rl.bhat

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    ΔL = (2n + 1)*λ/2. ........(1)
    Find the wavelength of the radio wave.
    The first destructive interference will occur when ΔL = λ/2.
    Now ΔL = sqrt(9.3^2 +x^2) - x...(2)
    Put ΔL = λ/2 and solve for x.
    Repeat the procedure for ΔL = 3λ/2, 5 λ/2......until x becomes negative.
     
  6. Mar 27, 2010 #5
    Thanks a lot

    I understand the proplem x is AP and I repeat the procedure to know how many time i have a destructive interfernce

    if there is anything i can help with
     
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