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If sound S played in point A reaches point B with volume V, after turning it off in point A and turning the same sound S in point B on, does it reach point A with the same volume V regardless of what obstacles are between? Ignore the noises.

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Yes. This is all to do with wave interaction. Wave sources and sinks operate independently of each other, even when waves interact with each other and with the medium through which they travel.

This is more a physics question, however it is highly appropriate to sound.

A very good explanation can be found at:

http://physics.bu.edu/~duffy/py105/WaveInterference.html

Additional information on "acoustic diodes" can be found here:

https://publishing.aip.org/publishing/journal-highlights/designing-acoustic-diode

Acoustic Diodes are objects that asynchronously affect sound depending on the direction of incidence.

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