Television viewers in rural areas often find that the picture flickers (fades in and out) as an airplane flies across the sky in the vicinity. The flickering arises from the interference between the signal directly from the transmitter and that reflected to the antenna from the airplane. Suppose the receiver is 36 km from the transmitter broadcasting at a frequency of 86.0 MHz and an airplane is flying at a height of about 600 m above the receiver toward the transmitter. The rate of oscillation of the picture’s intensity is 4 Hz.

(a) Determine the speed of the plane.

(b) If the picture’s intensity is a maximum when the plane is directly overhead, what is the exact height of the plane above the receiving antenna?