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=9.30m. An observer, P, is located on the x axis, a distance x=57.0m 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?

Now observer P walks along the x axis toward antenna A. What is P's distance from A when he first observes fully destructive interference between the two waves?

a)   Δφ = 1.51 rad , b)  x = 21.17 m

Explanation:

This is an interference problem, as they indicate that the distance AP is on the x-axis the antennas must be on the y-axis, the phase difference is

          Δr /λ = Δfi / 2π

          Δfi = Δr /λ 2π

          Δr = r₂-r₁

let's look the distances

         r₁ = 57.0 m

We use Pythagoras' theorem for the other distance

         r₂ = √ (x² + y²)

         r₂ = √(57² + 9.3²)

         r₂ = 57.75 m

The  difference is

         Δr = 57.75 - 57.0

         Δr = 0.75 m

Let's look for the wavelength

        c =  λ f

          λ = c / f

          λ = 3 10⁸ / 96.0 10⁶

          λ = 3.12 m

Let's calculate

         Δφ = 0.75 / 3.12 2π

         Δφ = 1.51 rad

b) for destructive interference the path difference must be λ/2, the equation for destructive interference with φ = π remains

           Δr = (2n + 1) λ / 2

For the first interference n = 0

           Δr = λ / 2

           Δr = r₂ - r₁

We substitute the values

        √ (x² + y²) - x = 3.12 / 2

Let's solve for distance x

          √ (x² + y²) = 1.56 + x

          x² + y² = (1.56 + x)²

          x² + y² = 1.56² + 2 1.56 x + x²

          y2 = 20.4336 +3.12 x

          x = (y² -20.4336) /3.12

          x = (9.3² -20.4336) /3.12

          x = 21.17 m

This is the distance for the first minimum

Explanation:

Check attachment for solution

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )