3. [25 points] A new radio station for the Baltimore area is being built near BWI. Its frequency conflicts with a radio station in Washington, D.C., so the proposal is to install two antennas and achieve a constructive interference toward Baltimore, and a destructive interference toward D.C. We will assume that the antennas are on a straight line connecting Baltimore and Washington, and thus we will use a one-dimensional coordinate system. The two antennas are separated by distance L (as shown on the figure) and emit signal at the same frequency w (and thus of the same wavelength A). The second antenna can also have an additional phase shift $20. to Washington, DC (destructive interference) (1) (2) x=0 x = L to Baltimore (constructive interference) +x The signals of the two antennas in the direction of Washington (x < 0) are: = E₁(x,t) Eo sin(-kr - wt) E2(x, t) Eo sin(-k(1- L) - wt + 020) And in the direction of Baltimore (1 > L): E₁(x,t) = Eo sin(kr - wt) E2(x, t) Eo sin(k(1 - L) - wt +420) Your goal is to help determine the parameters of this two-antenna system, L and 20. Many pairs of (L, 20) achieve this task, but you must select the one that results in the smallest possible value of L (since the land near BWI is expensive). (a) What is the condition for constructive interference toward Baltimore, i.e. for I>L? This should give you one equation for L and 20. (b) What is the condition for destructive interference toward D.C., i.e. for 1 < 0? This should give you another equation involving L and 20- (c) Solve these two equations for L. If you have kept integers in parts (a) and (b), now is the time to choose them so that L has the lowest possible (positive) value. (d) Now that you have L, what is 20?