Astronauts on the Lunar surface wish to establish real-time voice communication with a command module orbiting Earth. The straight-line center-to-center distance between Earth and the Moon is approximately 3.84×108m.
Consider the use of two possible communication methods: (1) speaking through an open microphone positioned on the Lunar surface, relying on sound waves traveling through space, and (2) transmitting a radio signal.
Answer the following questions.
(a) Determine the minimum possible time delay between sending a radio signal from the Moon and receiving it on Earth. Show your work and state any assumptions.
(b) Use physical reasoning to explain why voice communication based directly on sound waves is impossible across the same Earth–Moon distance, even if extremely sensitive microphones were placed at the receiver.
(c) Suppose the astronauts run a taut communication cable between the Moon and Earth and attempt to send mechanical vibrations down the cable at 6.0×103m/s. Calculate how long a signal would take to traverse the cable, and compare that time with your result from part (a).