Two antennas located at points A and B are broadcasting radi

Two antennas located at points A and B are broadcasting radio waves of frequency 107.0 MHz. The signals start in phase with each other. The two antennas are separated by a distance d = 10.1 m. An observer is located at point P on the x axis, a distance x = 93.0 m from antenna A. The points A P and B form a right triangle.

a) What is the phase difference between the waves arriving at P from antennas A and B? Enter your answer in radians (rad).

b) Now observer P walks along the x axis toward antenna A. What is P\'s distance from A when they first observe fully constructive interference between the two waves?

c) If observer P continues walking until they reach antenna A, at how many places along the x axis (including the place you found in the previous problem) will they find maxima in the radio signal due to constructive interference?

Solution

(1) =c/f , as c=3*10^8
= 3*10^8/107*10^6= 2.8037m
PB= (10.1^2+93^2)= 93.546
d= PB-PA= 0.546m
2.8037:0.546= 2:x
x= 0.8177[rad]

(2) as LAP=x , LBP=y , n=1 , n=2.8037m
y= x+2.8037 ----(1)
y= (x^2+10.1^2) ---(2)
(1)=(2)
x+2.8037= (x^2+10.1^2)

x= 10.011[m] approx

(3) n=2: n=2.8037*2= 5.6074m
x^2+64= (x+5.6074)^2

x= 2.90[m]