Solving the Problem of Plane Height for Destructive Interference

[atse1900]

Waves broadcast by a 1500-kHz radio station arrive at a home reciever by two paths. One is a direct path, and the second is by reflection off an airplane directly above the home receiver. The airplane is approximately 100 m above the home receiver, and the direct distance from the station to the home is 20 km. What is the exact height of the airplane if destructive interference is occurring? (Assume that no phase change occurs on rfelective from the plane.)

I have no idea how would you solve this problem. Can someone help me out please? Thanks. =].

 

[Astronuc]

To have destructive interfence at some point, the waves must be 180° out of phase, i.e. the maximum of one coincides with the minimum of the other. So the difference between path lengths must include one-half of the wave length, but not necessarily exactly one-half of a wavelength.