What is the mathematics behind the sound volume sensor?

Question

Mathematics

Good afternoon! There are sound volume sensors. When a certain threshold is exceeded, they notify about it. And what mathematics underlies them and where can I find it?

Answer 1

RMS - Standard deviation.
You are asking a question that can be answered with an accuracy of plus or minus slippers, because the sound intensity can be changed with an accuracy of pole-minus slippers - Some people need the accuracy of "yelling or not yelling", someone needs "well, here are the cymbals at the top in the drum part they tinkle somehow not like that. And what do you need?
Clumsily and physically, you can, for example, measure the signal power, that is, the energy that the sound wave brings to the microphone. To do this, you need to calculate the RMS readings of the ADC, which measures the voltage coming from the microphone.
Also, you can correct for uneven frequency response of the microphone, which will require the addition of a digital filter before calculating the RMS
And yet, you can take into account the unevenness of auditory perception to different frequencies, one more filter will be added.