1) MEASUREMENT ACCURACY OF INSTRUMENTS:
The transducer (microphone) and the ADC (audio interface) can provide a certain measurement accuracy, typically obtainable from the specifications, or better, from a calibration certificate traceable to the International System of Units (SI). In calibration these instruments are compared with references that are sufficiently more precise, but still have their uncertainty, and the measurement accuracy that they can provide can be roughly considered as the deviation found (error) plus the uncertainty of the reference.
It is often used to compensate the measurement with the inverse of the deviation (the use of the famous microphone calibration file) in order to improve its accuracy. This is a widespread practice in metrology, however, two things should still be considered:
a. The uncertainty of the reference from which it was calculated in deviation: if I detect an error of -5 and the associated uncertainty is +/-15, I cannot be sure that my compensation is bringing me closer to the true value. Conversely, if I have an error of -5 at an uncertainty of +/-1, then I am sure that by compensating with +5 I am improving my accuracy.
b. The accuracy defined in the specification by the instrument manufacturer: even where I have an uncertainty favorable to the application of the compensation, I should still take into account the accuracy defined by the manufacturer, because he has defined (or should) this parameter as a function of all the variables typically at play in the use of the instrument (e.g., temperature, humidity, etc.). So even if I have calibrated my instrument with an absurdly precise reference, very close to the Si standard, I should remember that this result is valid for those specific calibration conditions and could change as a function of them.
In addition to the above, other factors also affect the measurement accuracy of instruments. An analog instrument such as a microphone will have, for example, stability, noise, linearity, hysteresis, offset. While a digital instrument such as an ADC could have phase noise, resolution, rounding, truncation, interpolation. Even the software used contributes to the measurement uncertainty if it performs mathematical operations.
2) INFLUENCE OF PHYSICAL VARIABLES:
As can be deduced from the previous point, the variables involved in a measurement are multiple and it is often not possible to analytically quantify their contribution to the uncertainty. In the measurement of an audio system in a room we have variables such as temperature, humidity and noise that we cannot determine exactly how much they are influencing the physical quantity that we want to measure, nor the instruments that we are using. In these cases, to estimate the contribution of uncertainty we proceed statistically, repeating N times the measurements under the same conditions, or if desired, under varying conditions, so as to be able to then appropriately quantify the range within which my real value can be found.
3) INFLUENCE OF THE MEASUREMENT SETUP
The measurement we have to do here is really unfortunate. If I have to measure an electrical signal, I plug in the cable and measure. Few influences related to the setup. If I have to measure a signal that propagates by means of the variation of air pressure over time in a closed space... the influences related to the setup are many.
a. The room reflects the signal: the good thing is that the room effect is part of what I want to measure. The bad thing is that the room effect depends on the measurement point. So the uncertainty due to the reflections is very important, especially when our listening point is not extremely fixed at one point.
b. The orientation of the microphone: the microphone, although omnidirectional, introduces an alteration depending on the angle of reception of the signal in space. The uncertainty that this entails on the direct sound will probably be small (it is quite easy to position it at 0° or 90° with respect to the sound source), especially if I use a calibration file, but the reflected sound waves will have a different and unpredictable incidence. Therefore there will be a component of uncertainty linked to the signal depending on the incidence with which it arrived at the capsule.