Waves from a radio station with a wavelength of 900 m arrive at a home receiver a distance 50 km away from the transmitter by two paths.One arrives via a direct-line path and the second by reflection from a mountain directly behind the receiver.What is the minimum distance between the mountain and receiver such that destructive interference occurs at the location of the listener? Assume no phase change on reflection.
A) 675 m
B) 900 m
C) 450 m
D) 225 m

Question

Quizplus · Accepted Answer

Destructive interference occurs when the path difference is an odd multiple of half-wavelengths. The wavelength is 900 m, so half of that is 450 m. The path difference must be 450 m for the first instance of destructive interference. Since the wave travels to the mountain and back, the minimum distance to the mountain is 225 m (450 m / 2).

Waves from a Radio Station with a Wavelength of 900