Two antennas located at points A and B are broadcasting radio waves of frequency

Question

Two antennas located at points A and B are broadcasting radio waves of frequency 95.0 MHz, perfectly in phase with each other. The two antennas are separated by a distance d=12.40 m. An observer, P, is located on the x axis, a distance x=80.0 m from antenna A, so that APB forms a right triangle with PB as hypotenuse. What is the phase difference between the waves arriving at P from antennas A and B?

1. As P gets closer to A, the path length difference gets larger. What's the smallest path length difference that gives destructive interference?

2. If observer P continues walking until he reaches antenna A, at how many places along the x axis (including the place in the previous problem) will he detect minima in the radio signal, due to destructive interference?

Explanation / Answer

?L = (2n + 1)*?/2. ........(1)
Find the wavelength.
The first destructive interference will occur when ?L = ?/2.
Now ?L = sqrt(9.3^2 +x^2) - x...(2)
Put ?L = ?/2 and solve for x.
Repeat the procedure for ?L = 3?/2, 5 ?/2......until x becomes negative.

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