Two radio antennas separated by d $=302$ m$,$ 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 $=1,190$ m 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 $=400$ m 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$($i$)$