Two radio antennas send out signals that are in phase with each other. The anten

Question

Two radio antennas send out signals that are in phase with each other. The antennas are separated by a distance d=15.0 meters and emit signals with a wavelength of 3.00 meters. The point P is 100 meters away from antenna A.

a). What is the phase difference between the signals from the towers point P?

b). What minimum and maximum does point P sit between?

c). Is the signal at point P strong or weak? Explain you answer.

I have the answers to these question, and I will post below. Please show your work and equations used so I am able to understand how to get to the final ansers.

a). 2.32 radians

b). Between the central maximum and the first minimum

c). Relatively weak as it is closer to the first minimum than the central maximum

Explanation / Answer

a)
from figure

rA = 100

rB = sqrt(100^2 + 15^2)

= 101.11 m

path diffrence = 101.12 - 100

= 1.1 m

we know phase diffrence = (2*pi/lamda)*path diffrence

= (2*pi/3)*1.11

= 2.32 rad

b) we know for distructive interefrence, path diffrence = lamda/2 = 3/2 = 1.5 m

here, path diffrence is close to lamda/2.

so, Between the central maximum and the first minimum

c) As I explined in part b) at point P the signal will be weak.

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