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In the footage taken by U.S. astronaut Terry Virts during spacewalk (EVA) on the International Space Station on 25.02.2015, sounds can be heard while in space.

I can understand "shaking" sounds while moving the GoPro can be caused by the microphone membrane actually rattling, hence recording a sound. What confuses me is that at some point the GoPro camera is left alone and pointing to a (stunning) view of the station and Earth: during that part, is like the sound of the moving radar - or something else mechanical - can be heard.

Also if that is indeed the sound of the radar moving or something else mechanical moving, and if the sound is propagated via the exterior of the station, wouldn't this imply a very high noise inside the ISS all the time?

Ref: the footage, manually select "7 US-EVA30-Highlights 720p", minute 1:30

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You correctly assumed that sound in space does not propagate ( the density of gas molecules is between 1 per cubic meter and 1 per cubic centimeter, too low to efficiently propagate sounds ).

But the Camera is mechanically attached to the space suit, which contains various mechanical parts, like a thermal control system to manage the temperature inside the suit, some devices to collect Urine and others to vent air. Those units obviosuly imply mechanical objects like fans and pumps which produce noise (that will be mechanically transmitted to the camera through the suit itself).

Finally, inside the ISS there indeed is a very high level of noise pollution. According to NASA sources, until some years ago the noise level would hit 70 dBA in the day quarters and 64 in the sleep quarters, and astronauts used to counter that by wearing ear plugs. I have read somewhere that now the noise level has been lowered, but cannot find a source.

Suit: http://en.wikipedia.org/wiki/Extravehicular_Mobility_Unit

Noise level: https://www.nasa.gov/mission_pages/station/research/experiments/279.html

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