Two identical sound sources have a frequency of 500 Hz. The coordinates of the sources are (0, 1 m) and (0, 1 m) A detector 80 m from the origin is free to revolve in the xy plane with a radius of 80 m. The first maximum in intensity is detected when the detector is at (80, 0) m.

(a) Find the coordinates of the detector for the first five maxima in order of decreasing positive values of x.

(b) Find the coordinates for the first four minima in order of decreasing positive values of x subject to the condition x₂ + y₂ = 80 m.