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Const@ntine

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## Homework Statement

A ship floats across the coat, at a distance d = 600 m from it. The radio of the ship receives simultaneously signals of the same frequency from RadioTowers A & B, which are L = 800 m apart. At Point G (Γ), the two waves confluent in a strengthening way, where G's (Γ) distances from A & B are the same (r

_{A}= r

_{B}). At point D (Δ), which is right across B, the signal reaches its First Minimum. Find the wavelength λ.

## Homework Equations

Δr = n*λ , n = 0,1,2,3... (Strengthening-A'=2)

Δr = n*(λ/2), n = 1,3,5... (Weakening-A'=0)

## The Attempt at a Solution

When the book says "First Minimum arrives at..." in every case it means Δr = n*λ/2 with n = 1. So i went ahead and found rA & rB for Δ through the forming triangles, put them in the above formula and got λ = 140 m. Which is wrong. I kinda figured that since I didn't use the stuff for Γ, but anyway. I turned back and saw that the answer was λ = 800 m. Which is a pretty big number.

So I thoughout of it this way: The signals arrive at Γ, the composite wave starts the way a y = Asin(...) wave would (no Initial Phase so it goes from "zero" to +A and then back down) and at Δ it's where the composite wave reaches the "horizontal axis" again, ie it covers λ/2 in length. Through that and the info about Γ (used the rs to find ΑΓ = ΓΒ = 400 m) I did λ/2 = 400 m <=> λ = 800 m

Now the result is correct, but I have no idea if the whole thing has any logic behind it. I was just trying stuff until I got the correct result. I mean, in every exercise thus far "First Minimum" just means Δr = λ/2.

Any help is appreciated!