Question

when television and radio waves are broadcast across the landscape, they can reflect off of features like mountains, or even airplanes, and interfere. suppose 75 MHz television signal from a distant source are being detected at a receiver. some of the signal is reflected from an airplane that is 122 m directly above the receiver. what kind of interference occurs? assume a lambda/2 phase change occurs upon reflection.

Answer 1

Given, frequency = 75 MHz = 85 times 10^6 Hz Speed of electromagnetic wave in vacuum = 3 times l0^8 m/s Let's find wavelength, lambda = c/f = 3 times 10^8 m/s/75 times 10^6 Hz = 4 m Concept - for constructive interference, path difference should be integral multiple of wavelength like delta X = n lambda For destructive interference, path difference should be odd integral multiple of half of wavelength like delta X = (n + 1/2) lambda Here n = 1, 2, 3, etc for both cases. Now path length of reflected wave = 122m + lambda/2 = 122m + 4/2 m Path length = 124m Now, let's find total number of complete waves that can be formed with this path length of reflected wave. N = 124 m/lambda = 124 m/4m = 31 = integers The path length wave that comes out from the source to receiver is also be in integral multiple of wavelength. So path difference between reflected and the waves comes out from source will be integral multiple of wavelength. So, at receiver there must be constructive interference.