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?

Answer 1

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

      $z = \frac{ 5 -3 }{2}$

=>   $z = 1 \ m$

=>    $z = (1 \ m , 4 \ m )$