[robocat]

You are incorrectly assuming sound is additive, but it isn't.

Sound is non-linear as sound gets louder - sound wave volume is physically limited because the low of the sound wave can't be lower than vacuum.

Another non-linearity is air cannot transmit frequencies higher than some limit.

Another is that sound has a noise floor depending on the temperature of the gas (noise like rain on a roof?).

There are surely other gross non-linearities.

Those non-linearities mean you can't add or subtract some sounds, and you can't assume commutativity.