Waves from a radio transmitter travel by two paths to a receiver 14.1 km away - a direct path and a reflected path off a mountain. The question asks to calculate the minimum distance between the mountain and receiver that would cause destructive interference at the receiver. The answer shows that the path difference must be half a wavelength for destructive interference, and calculates that minimum distance as 90.5 meters.

1. Question:Wavesfromaradio stationhave a wavelengthof 362 m.Theytravel by twopaths to a home
receiver14.1 km fromthe transmitter.One pathisa directpath,and the otherisby reflectionfroma
mountaindirectlybehindthe home receiver.Whatis the minimumdistance fromthe mountaintothe
receiverthatproducesdestructiveinterferenceatthe receiver?
Answer:Distance frommountaintohouse =d
wave pathdifference =2d
min.path difference fordestructive interference =½ λ
2d = ½ λ
d = λ/4 -> 362/4 ->d= 90.5 m