2) An FM radio transmitter, operatingat a frequency of 120 MHz, is atop a 100-mt

Question

2) An FM radio transmitter, operatingat a frequency of 120 MHz, is atop a 100-mtower. An airplane

is in flight over the ocean at analtitude of 2000 m. Radio waves reach the airplane directly fromthe

transmitter and by reflection from thesurface of the ocean. When the airplane is 86 km fromthe

tower, the pilot observes that radioreception has faded due to destructive interference of thewaves

in the two paths. Assume the wavereflected from the ocean surface has undergone ahalf-wave

phase shift. In Fig. 35.1a, the wavesof the reflected path arrive at the airplane delayed, withrespect

to the direct path. The time intervalof this delay, in ns, is closest to:

2)

A) 14 B) 20 C) 22 D) 16 E) 18

Explanation / Answer

the frequency of the FM radio transmitter is f = (c/) ---------(1) the frequency of the wave reflected from the surface of oceanis f1 = (c/1) ---------(2) (2)/(1) (f1/f) = [(c/1)/(c/)] =(/1) or ((1/T1)/(1/T)) =(/1) or (T/T1) = (/1) 1 = (/2) or (T/T1) = (/(/2)) = 2 or T1 = (T/2) The time interval of this delay is t = T - T1 = T - (T/2) = (T/2) T = (1/f) where f = 120 MHz = 120 * 106 Hz or t = (1/120 * 106) = 8.33 * 10-9s = 8.33 ns

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