The broadcast antenna of an AM radio station is located at the edge of town. The

Question

The broadcast antenna of an AM radio station is located at the edge of town. The station owner would like to beam all of the energy into town and none into the countryside, but a single antenna radiates energy equally in all directions. FIGURE CP21.84 shows two parallel antennas separated by distance L. Both antennas broadcast a signal at wavelength lambda, but antenna 2 can delay its broadcast relative to antenna 1 by a time interval Delta t in order to create a phase difference Delta phi 0 between the sources. Your task is to find values of L and Delta t such that the waves interfere constructively on the town side and destructively on the country side.

Explanation / Answer

the phase difference between 1 and 2. outside. phi1 - phi2 = -L*2pi/lamda + ?t*2pi/T where T=lamda/c. so phi1-phi2 = -L*2pi/lamda + ?t*2pi*c/lamda = (L-?t*c)*2pi/lamda. inside. phi1 - phi2 = L*2pi/lamda + ?t*2pi*c/lamda = (L+?t*c)*2pi/lamda. so lets (L-?t*c)/lamda = k1+1/2 (L+?t*c)/lamda = k2 (k1, k2, = 0, 1, ,2 ) so 2L=lamda*(k1+k2+1/2). so L=lamda*(k3+1/2)/2=lamda*(k3/2+1/4). and ?t*c=lamda*(k1-k2-1/2)/2=lamda*(k4/2-1/4). where k3=0,1,2 ... k4=0,1,2.... (k3 may difference from k4)

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