Question

Two coherent sources of radio waves, A and B, are 5.00 metersapart. Each source emits waves with wavelength 6.00 meters.Consider points along the line connecting the two sources.

a) At what distance from source A is there constructiveinterference between points A and B?
b) At what distances from source A is there destructiveinterference between points A and B?

Answer 1

given,

distance between A and B is equal to 5 m

let x be the distance of loud speaker from the source A

For constructive interference, path difference = mλ

x - (5 - x ) = 0 , for m = 0

2 x - 5 = 0

2 x = 5

x = 2.5 cm

For destructive interference

`|x - (5 - x )| = (2 m + 1)(\lambda)/(2)`

m = 0

`|2x - 5| = (\lambda)/(2)`

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

`\pm(2x - 5) = 3`

x = 4 , 1 cm