Two radio antennas separated by $d=270m,$ as shown in the figure below, simultaneously broadcast identical signals at the same wavelength. A car travels due north along a straight line at position $x=1,200m$ from the center point between the antennas, and its radio receives the signals. Hint: Do not use the small$-$angle approximation in this problem.

$($a$)$ If the car is at the position of the second maximum after that at point $O$ when it has traveled a distance of $y=400m$ northward, what is the wavelength of the signals?

$m$

$($b$)$ How much farther must the car travel from this position to encounter the next minimum in reception?

m