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Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon, and transformed back into sound on a speaker inside the astronaut’s space suit. This sound was picked up by the microphone in the space suit (intended for the astronaut’s voice) and sent back to Earth as a radio echo of sorts. If the round-trip time was 2.60 s, what was the approximate distance to the Moon, neglecting any delays in the electronics?
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Final Answer

$3.90 \times 10^8 \textrm{ m}$

Solution Video

OpenStax College Physics Solution, Chapter 24, Problem 25 (Problems & Exercises) (1:16)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Radio-emissions to an astronaut standing on the moon had an effect where the light was emitted from earth and then it goes into the moon… the astronaut’s space suit and then the space suit turns the radio waves into a sound signal that’s emitted by the speakers inside their helmet and then the microphone in their helmet picks up that sound that is emitted by the speaker and in turn relays it back to earth and so this signal has a round trip of two times the distance between Earth and the moon and so we have 2 times <i>d</i> equals the speed of light multiplied by the total time it takes to this round trip. This assumes that the electronics in the astronaut’s space suit are instantaneous, we could neglect the time it takes for, to turn the radio waves into a sound wave and then also sound wave back into a radio wave on the microphone end. So, we will divide both sides by 2 and we have distance between earth and the moon then is 3 times 10 to the 8 meters per second times 2.60 seconds for this round trip to happen divided by 2 and that works out to 3.90 times 10 to the 8 meters.