Wavelength interference

Question

Transmitter and receiver 50 m above ground and 600 m apart Ground is level between them and a (sign for wavelength)/2 phase shift occurs upon reflection. What are the longest wavelengths that interfere constructively and destructively. Okay, I need help on how to do this I have the equations but I don't know which figures go where. Anything is greatly appreciated.

Answer 1

Let one wave go directly from transmitter to the receiver and another wave that comes from the transmitter to ground and reflect from it and go to the reciever. If  limbda/2 phase shift is introduced to the reflected wave. then the two waves will interfere distructly if the path difference between the two waves is integer multiple of limbda. (remember that the reflection has introduced limbda/2 phase shift). so,

path difference = n * limbda

where path travelled by the reflected waves is

= 600 - 2{square root[(50)^2 + (300)^2}]  = 169 m

The longest wavelength happens for n = 1. so longest wavelength that interfere distructly is 169 m

for cosnstructive interfere the path difference is integer multiple of limbda/2 so from the above relation it comes out to be 339 m