The
quandary presented here arises more as a result of the way you have
worded the
question than as a matter of
scientific principle.
There is indeed a threshold of detection, but it depends on the sensitivity of the microphone, the resolution of the analog to digital converter, and all the noise characterisitcs of every bit of circuitry in between the sound source and the ADC.
As an electrical engineer, all I can really say is that this is one of those areas where one has to make generalizations and assumptions in order to produce a meaningful answer.
As I said in my opening sentence, the question, as you have posed it, does not adequately define a solvable system. You have asked a question of this sort:
The point being, while these are questions, their lack of solution has more to do with
semantics than with any
fundamental mystery or
failure of
analysis. In other words, this "
puzzle" is a
word game, not a
problem of science.