Is it logarithmic, linear, something else entirely???
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Since sound moves in 3 dimensions, the raw power of the sound will be related by an inverse square to the distance of the source. Since humans perceive sound in a logarithmic scale to its raw power, it is logarithmic as well.
So first, inverse square from the distance to the source. And then, logarithmic to the resulting power of the sound.
Adding to the other answers, loudness (sound volume as judged by people) doubles with roughly every 8 to 10 decibel increase in intensity, meaning a factor of 6 to 10. Since sound intensity changes according to a square law with distance, that translates to loudness doubling with distance reducing by a factor of 2.5 to 3.2; call it roughly 3.
In an anechoic environment, the midrange frequencies decreases by 3dB for every doubling of distance. Bass and treble frequencies are a bit different (bass lasting longer and treble lasting less).
However, we rarely are in an anechoic environment. If outside on dirt then it’d be close, but outside on concrete and even moreso being in a small & reflective room, sound will persist more.
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