Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source emits waves with wavelength 6.00 meters. Consider points al

Question

Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source emits waves with wavelength 6.00 meters. Consider points along the line connecting the two sources.Required:a. At what distance from source A is there constructive interference between points A and B?b. At what distances from source A is there destructive interference between points A and B?

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RI SƠ 7 months 2021-08-11T13:51:26+00:00 1 Answers 0 views 0

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    2021-08-11T13:53:06+00:00

    Answer:

    a

        z= 2.5 \ m

    b

       z =  (1 \ m ,  4 \ m )

    Explanation:

    From the question we are told that

         Their distance apart is  d =  5.00 \ m

          The  wavelength of each source wave \lambda =  6.0 \ m

    Let the distance from source A  where the construct interference occurred be z

    Generally the path difference for constructive interference is

                  z - (d-z) =  m \lambda

    Now given that we are considering just the straight line (i.e  points along the line connecting the two sources ) then the order of the maxima m =  0

      so

            z - (5-z) =  0

    =>     2 z - 5 =  0

    =>     z= 2.5 \ m

    Generally the path difference for destructive  interference is

               |z-(d-z)| = (2m + 1)\frac{\lambda}{2}

    =>         |2z - d |= (0 + 1)\frac{\lambda}{2}

    =>        |2z - d| =\frac{\lambda}{2}

    substituting values

              |2z - 5| =\frac{6}{2}

    =>      z  =  \frac{5 \pm 3}{2}

    So  

          z =  \frac{5 + 3}{2}

          z =  4\ m

    and

          z =  \frac{ 5 -3 }{2}

    =>   z =  1 \ m

    =>    z =  (1 \ m ,  4 \ m )

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