An FM radio transmitter operating at a frequency of 120 MHz

An FM radio transmitter, operating at a frequency of 120 MHz, is atop a 100m tower. An airplane is in flight over the ocean at an altitude of 2000m. Radio waves reach the aiplane directly from the transmitter and by reflection from the surface fo the ocean. When the airplane is 86 km from the twoer, the pilot observes that radio reception has faed due to destuctive interfernece of the waves in the the two paths. Assume the wave reflected from the ocean surface has undergone half-wave phase shift. In the figure above, the waves of the reflected path arrive at the airplane delayed, with respect to the direct path. The time interval of this delay, in ns, is closest to?

Solution

we know

phase difference =(2 pi/lambda )* path difference

here path difference=100m

phase difference= {2*pi /( c/frequency)}*100

phase differnce= {2*pi/(0.025*10² )}*100=80*pi

phase difference =(2 pi/T)* time interval

T=1/f=1/ (120*10⁶ )=8.33*10^-9sec

given phase difference= 80*pi

then

80*pi = {2*Pi/(8.33*10^-9)}* time delay

80=0.240*10⁹ *time delay

time delay=333.33*10^-9=333.33ns