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

a

`z= 2.5 \ m`

b

`z = (1 \ m , 4 \ m )`

Step-by-step 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)(\lambda)/(2)`

=>
`|2z - d |= (0 + 1)(\lambda)/(2)`

=>
`|2z - d| =(\lambda)/(2)`

substituting values

`|2z - 5| =(6)/(2)`

=>
`z = (5 \pm 3)/(2)`

So

`z = (5 + 3)/(2)`

`z = 4\ m`

and

`z = ( 5 -3 )/(2)`

=>
`z = 1 \ m`

=>
`z = (1 \ m , 4 \ m )`