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# minimum distance from the mountain to the receiver

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Waves from a radio station have a wavelength of 262 m. They travel by two paths to a home receiver 14.1 km from the transmitter. One path is a direct path, and the other is by reflection from a mountain directly behind the home receiver. What is the minimum distance from the mountain to the receiver that produces destructive interference at the receiver? (Assume that no phase change occurs on reflection from the mountain.)

## SOLUTION This solution is FREE courtesy of BrainMass!

Since the mountain is directly behind the home receiver, the path difference in the two waves received at the home is
delta = 2d, where d is the distance for the home to the mountain.
Neglecting any phase change upon reflection, the condition for destructive interference is
delta = (m +1/2)*lamda, with m = 0, 1, 2,..
so the minimum distance from home to the mountain is when the first destructive interference fringe to occur at m =0
delta_0 = (0 + 1/2)*lamda = 0.5*lamda
2d_min = delta_0
d_min = 0.5*lamda/2
d_min = 0.5*262/2 = 65.5 m
the minimum distance from home to mountain is 65.5 m.

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