# Destructive Interference when walking toward an antenna

#### skibum143

1. Homework Statement
Two antennas located at points A and B are broadcasting radio waves of frequency 96.0 MHz, perfectly in phase with each other. The two antennas are separated by a distance d=12.40m. An observer, P, is located on the x axis, a distance x=55.0m from antenna A, so that APB forms a right triangle with PB as hypotenuse.

If observer P starts walking until he reaches antenna A, at how many places along the x axis will he detect minima in the radio signal, due to destructive interference?

2. Homework Equations
Destructive interference = lambda / 2
lambda = c/f

3. The Attempt at a Solution
Since lambda is 3.125 m (3E8 / 96MHz), I thought the total number of times the observer would experience destructive interference would be once every wavelength (where it's lambda / 2) so I took 55 / 3.125 and got 17.6, which would produce 18 destructive interferences. This is incorrect, not sure what I'm doing wrong. Picture is attached. Thanks!

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#### Redbelly98

Staff Emeritus
Science Advisor
Homework Helper
The picture is not attached, but the description is pretty clear so we can get the idea.

Your idea of when destructive interference happens is a little mixed up. The difference in the distances to each speaker must equal 0.5λ, 1.5λ, 2.5λ, etc. (It's not just the distance to antenna A, and ignoring antenna B, as you are saying.)

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