You have been hired to design a system that allows airplane pilots to make instr

Question

You have been hired to design a system that allows airplane pilots to make instrument landings in rain or fog. You've decided to place two radio transmitters 50 m apart on either side of the runway. These two transmitters will broadcast the same frequency but exactly out of phase with each other. This will cause a nodal line (perfect destructive interference) to extend straight along and off the end of the runway (you may want to sketch this and demonstrate that this is true). As long as the airplane's receiver is silent, the pilot knows she's directly in line with the runway. If she drifts to one side or the other, the radio will pick up a signal and sound a warning beep. To have sufficient accuracy, the first intensity maxima need to be 60 m on either side of the nodal line at a distance of 3 km along the nodal line from the transmitters. What frequency should you specify for the transmitters?

Explanation / Answer

distance between node and antinode is 60 m = wavelength/4

so wavelength = 60 x 4= 240 m

as speed of sound wave is 346 m/s

frequency = 346/240= 1.44 Hz

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