Radio waves in phase

Question

consider two antennas radiating 6.0 MHz radio waves in phase with each other. They are located at points S1 and S2 (on an x axis), separated by a distance d=175 m. What are the first three points on the y axis where the signals from the two sources will be out of phase (crests of one meet troughs of the other)?

Answer 1

Wavelength

λf = c = 3*10⁸m/s (speed of light)

λ = c/6M = 50 m

You don't say where they are on the x axis, I'll assume one is at 0

you need to find a point on the y axis where the distances to the far point is 25 + 50N while the distance to the near point is 50M

First solution is x=0 y=0

now move up the y axis, try y=50, and it won't work because distance is

√(50² + 175²) and that is not a multiple of 25

and neither are any other ones I can see.

probably can be proved by considering:

√((50+N)² + 175²) = z = 25 + 50M

Ans: only one solution at x=0, y=0

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