Question

3. FM radio waves from a distant tower pass through a relativelysmall gap (width b) between two very large buildings that areopaque to radio waves. (Assume that the radio waves are plane-wavesby the time they reach the gap, and their direction of travel isexactly perpendicular to b.) You walk along a street (shown here asthe x-axis) at distance s from the gap, perpendicular to thedirection the waves are traveling.




a. Suppose that b = 12.5 m, s = 20.0 m, and the wavelength of theradio waves is 2.897 m. As you walk along the x-axis from –xmax =–30.0 m to +xmax = 30.0 m while carrying your portable radio, atwhat positions will you discover total destructive interference ofthe radio waves? Find them all. Show your work. (Use the abovediagram if needed. You may use the symmetry of the situation tosave some work, but explain your reasoning as necessary.)

b. (3 pts.) Calculate the frequency of the FM station. Show yourwork.

c. (4 pts.) Suppose that your portable radio uses a series L-R-Ccircuit to tune in to the desired radio station. As you rotate thetuner dial, you adjust the value of a variable capacitor, C. If Lis fixed at a value of 4.80 µH and R is fixed at 2.2 Ω, find thevalue of capacitor C when the radio is tuned to the station in part(b). Show your work.