# Problem: Two out-of-phase radio antennas at X =  ± 300m on the x-axis are emitting 3.0 MHz radio waves. Is the point (x,y) = (300m, 800m) a point of maximum constructive interference, perfect destructive interference, or something in between?

🤓 Based on our data, we think this question is relevant for Professor Eberle's class at Dallas College.

###### FREE Expert Solution

Relationship between speed, frequency and wavelength:

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{f}}{\mathbf{\lambda }}}$

Condition for constructive interference:

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

Condition for destructive interference:

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

Where Δx is the path difference and m is an integer.

m = 1,2,3...

The above conditions apply when the sources are coherent (in-phase).

When the sources are out of phase, the conditions are reversed. That is Δx = mλ describes condition destructive interference.

###### Problem Details

Two out-of-phase radio antennas at X =  ± 300m on the x-axis are emitting 3.0 MHz radio waves.

Is the point (x,y) = (300m, 800m) a point of maximum constructive interference, perfect destructive interference, or something in between?