An Earth-observing satellite transmits a continuous radio signal toward Earth while orbiting at an altitude of 700km above the planet’s surface. The radio wave has a period of 1.0ns as measured in the satellite frame. Assume that, for the purposes of this problem, the wave travels through space and the atmosphere at exactly 3.00×108m/s.
(a) Determine the frequency of the transmitted radio wave.
(b) Calculate the wavelength of the radio wave.
(c) Compute the number of complete wave cycles present, at any instant, along the straight-line path from the satellite to a point directly beneath it on Earth’s surface.
(d) During a calibration test, mission controllers command the satellite to switch to a signal whose period is 0.80ns. Quantitatively determine how the answers to parts (b) and (c) will change. Discuss whether the change in wavelength is likely to have any significant impact on the satellite’s ability to transmit data through the atmosphere, and justify your conclusion.