Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source

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.
At what distance from source A is there constructive interference between points A and B?
At what distances from source A is there destructive interference between points A and B?
Note that there will be two separate interference fringes between point A and point B. Enter your answers in ascending order separated by a comma.

Explanation / Answer

at a distance x the two are in constructive interference

sA = x

sB = 5-x

wavelength = ? = 6m

for constructive interfereence path difference = n?

n = 0 , 1 ,2 ,3 ,4..

for n= 0

sA - sB = 0

x - (5-x) = 0

2x - 5 = 0

x = 5/2 = 2.5 m <----answer

+

part B)

for destructive interference path diffeence = n*?/2

n = 1 , 3 , 5 , 7......

n = 1

sA - sB = 6/2 = 3

x - (5-x) = 3

2x -5 = 3

2x = 8

x = 4 m <-----answer

at a distance of 4 m there is destructive interference

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