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

###### FREE Expert Solution

Path difference for constructive interference,

$\overline{){\mathbf{∆}}{\mathbf{x}}{\mathbf{=}}{\mathbf{m}}{\mathbf{\lambda }}}$

Path difference for destractive interference,

$\overline{){\mathbf{∆}}{\mathbf{x}}{\mathbf{=}}{\mathbf{\left(}}{\mathbf{m}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\right)}}{\mathbf{\lambda }}}$

(a)

Separation of points A and B, L = 5.00 m

Let A be at x = 0 and B be at x = 5.00 m.

Sum of the radial distance, rA + rB = 5.00 m

rB = 5.00 - rA

Path difference, |Δx| = rA - rB = ( rA - (5.00 - rA ) = 2rA - 5.00

The displacement |Δx| can be positive or negative based on the reference point.

mode, m = 0

###### Problem Details

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

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?