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. find a) at what distance from source a is there constructive interference between points a and b? (answer in meter) 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.]

a) 2.5 m

The condition for constructive interference to occur is

(1)

where

dA is the distance of the point from source A

dB is the distance of the point from source B

m is an integer number

is the wavelength of the wave

We immediately notice that solutions to the equation are only possible if m=0: otherwise, the difference between dA and dB would be at least 6.0 m, which is impossible since the two sources have a separation of 5.0 m (and we are considering only points between the two sources). Therefore we have

So, constructive interference occurs halfway between the two sources.

b) 1 m, 4 m

The condition for destructive interference to occur is

(1)

As before, solutions are only possible for m=0, otherwise the point would not lie between the two sources.

So for m=0, we have:

So, the two possible solutions are (using )

and

So, the solutions are dA= 1 m and dA=4 m.