Path difference for constructive interference,

$\overline{){\mathbf{\u2206}}{\mathbf{x}}{\mathbf{=}}{\mathbf{m}}{\mathbf{\lambda}}}$

Path difference for destractive interference,

$\overline{){\mathbf{\u2206}}{\mathbf{x}}{\mathbf{=}}{\mathbf{(}}{\mathbf{m}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{)}}{\mathbf{\lambda}}}$

**(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, r_{A} + r_{B} = 5.00 m

r_{B} = 5.00 - r_{A}

Path difference, |Δx| = r_{A} - r_{B} = ( r_{A} - (5.00 - r_{A} ) = 2r_{A} - 5.00

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

mode, m = 0

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?

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