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IM, absolute polarity, and recording

Posted by psn (A) on November 19, 2021 at 13:08:24

Imagine this experiment:

Two independent audio signal generators, "A" and "B", present both their signals to the input of a single amplifier.

"A" produces a sine wave of frequency 70Hz
"B" produces a sine wave of frequency 1100Hz

The amp comprises two gain stages so phase is inverted twice.
The two frequency components in the signal are voltage summed and maintain registration with respect to each other - no intermodulation distortion.

Then, a single speaker direct radiator is connected. The paper moves forward and backward at 70Hz while vibrating at 1100Hz, so the 1100Hz is acoustically Doppler shifted sharp when the paper is moving forward into the room air, and shifted flat when receding back from the room air... the speaker exhibits intermodulation distortion.

Now imagine this version of the experiment:

Two independent audio signal generators, "A" and "B", each present their signal to an independent amp, each amp is connected to its own independent speaker... so two separate systems "A" and "B", each comprised of a generated signal, amp, and speaker.

"A" produces a sine wave of frequency 70Hz
"B" produces a sine wave of frequency 1100Hz

Each amp comprises two gain stages so phase is inverted twice.

This time a single microphone is used to record the sound from both speakers. That recording is later played back through a single amp to a direct radiator. The wiring to the recording microphone and the wiring to the later playback speaker are such that the over-pressure that made the microphone diaphragm displace inward will make the playback speaker's paper displace outward and present an over-pressure to the air in the room, and vice versa...

The diaphragm of the microphone moved forward and backward at 70Hz which made the diaphragm encounter the 1100Hz while in motion moving back and forth, generating the signal frequency of the 1100Hz sharp when moving toward the sound source and flat when moving away from it. Doppler shift was recorded from the diaphragm's motion so that shift will be present in the signal of the later playback amplifier and speaker.

Now during playback, the single speaker direct radiator paper moves forward and backward at 70Hz while vibrating at 1100Hz, but since the Doppler shift is in the signal, the flattened Doppler shifted part of the signal is when the paper is moving forward into the room air, and the sharpened part of the shift is when receding back from the room air... the speaker motion corrects the shifts recorded in the signal
because of the same mechanics by which it was captured by the microphone. The sound does not exhibit intermodulation distortion.

If you're still with me, consider one more version (but it's simple):

Same as the last on, but the playback speaker's wires are reversed!

Now during playback, the single speaker direct radiator paper moves forward and backward at 70Hz while vibrating at 1100Hz, but since the Doppler shift is in the signal, the sharpened Doppler shifted part of the signal is when the paper is moving forward into the room air, and the flattened part of the shift is when receding back
from the room air... the speaker motion doubles the shifts recorded in the signal and the sound exhibits twice the intermodulation distortion.

Questions:

- Have I thought this through correctly, are my assumptions and understanding right?

- Is this something that recording studios routinely take into account when setting up mics, managing tracks, monitoring playback, and generally engineering recording of music? Or do they not think about it?

- It seems to me that even with complicated modern recording methods with multiple mics and tracks and such, there could be best practice standards that would result in a world where absolute polarity of speaker connection would ensure best sound. But is it the case that none of this was ever worked through so that now it's generally all mixed up and random? Individual songs on the same album may sound better with polarity one way or the other, an incidental artifact or accident of chance in the studio?

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