Waves from a radio station with a wavelength of 644 m arrive at a home receiver a distance 50 km away from the transmitter by two paths.One is 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)161 m
B)322 m
C)483 m
D)644 m
E)1290 m

Question

Quizplus · Accepted Answer

For destructive interference to occur, the path difference between the two waves must be an odd multiple of half the wavelength, i.e., (2n + 1)λ/2, where n is an integer starting from 0. For the minimum distance, we use n = 0, which gives us λ/2. The wavelength λ is 644 m, so λ/2 = 322 m. However, since the wave reflects off the mountain, the actual path difference is twice the distance between the receiver and the mountain. Therefore, the minimum distance between the mountain and receiver is 322 m / 2 = 161 m.

Waves from a Radio Station with a Wavelength of 644