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Don't use the word loudness, because that is a psychoacoustic personal feeling. Look for sound pressure.

The sound pressure decreases with distance r in a free field (direct field).

The next question is. How does the sound decrease with increasing distance? After which law?

The sound pressure p diminishes with distance after the 1/r law. Sound pressure decreases inversely as the distance increases with 1/r from the sound source. The Sound pressure level (SPL) decreases by (−)6 dB per doubling of distance from the source to 1/2 (50 %) of the sound pressure initial value.

Equations: p2 / p1 = r1 / r2 and p2 = p1 x r1 / r2 or r2 = r1 x p1 / p2

p1 = sound pressure 1 at reference distance r1 from the sound source.

p2 = sound pressure 2 at another distance r2 from the sound source.

Scroll down to related links and look at "How does the sound or the noise decrease with distance?"

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Q: What happen to the loudness of sound as the distance incrase between a person and the source of the sounds?
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