Young's double-slit experiment underlies the instrument landing system used to guide aircraft to safe landings when the visibility is poor. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggest in the fig- ure. Two radio antennas A, and A., separated by 40.0 m, are positioned adjacent to the runway. The anten- nas broadcast single frequency, 30.0 MHz, coherent radio waves. 40 m A2 (a) Find the wavelength of the waves. The pilot “locks onto" the strong signal radiated along an inter- ference maximum and steers the plane to keep the received signal strong. If she detects the central maximum, the plane will have the right heading to land when it reaches the runway. (b) Suppose instead that the plane is flying along the first side maximum, one maxima from the central How far to the side of the runway centerline is the plane when it is 2.00 km from the antennas? (c) It is possible to tell the pilot she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as 3/4). Explain how this two-frequency system would work, and why it would not necessarily work if the frequencies were related by an integer ratio.

Young's double-slit experiment underlies the instrument landing system used to guide aircraft to safe landings when the visibility is poor. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggest in the fig- ure. Two radio antennas A, and A., separated by 40.0 m, are positioned adjacent to the runway. The anten- nas broadcast single frequency, 30.0 MHz, coherent radio waves. 40 m A2 (a) Find the wavelength of the waves. The pilot “locks onto" the strong signal radiated along an inter- ference maximum and steers the plane to keep the received signal strong. If she detects the central maximum, the plane will have the right heading to land when it reaches the runway. (b) Suppose instead that the plane is flying along the first side maximum, one maxima from the central How far to the side of the runway centerline is the plane when it is 2.00 km from the antennas? (c) It is possible to tell the pilot she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as 3/4). Explain how this two-frequency system would work, and why it would not necessarily work if the frequencies were related by an integer ratio.