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According to Ohm’s Law of Acoustics, the ear is phase insensitive due to its resonant structure. For example, changing the phase angle of the 3rd harmonic of a note drastically changes the shape of a waveform - but the ear cannot detect it.

If I play a note on my bass and feed it into stereo headphones as a mono signal, it centres in the middle of my head. If I invert the polarity of one channel, it changes the phase angle of each harmonic component by 180 deg. The puzzle is: I would expect the signals to cancel. Instead it appears all over my head like surround sound. Why is that? That’s why, if I practice on headphones, I invert one channel - I like it.

Update 1: If I add two electrical signals, one the inverse of the other, they cancel to give nothing. If I add two sound waves, one the inverse of the other, they should cancel. It’s this cancellation that causes beating between two close frequencies. This doesn’t happen with one such signal in each ear.

Update 2. Apologies for all the editing. Thanks to the discussion, I realise I’m confusing two issues. One is to do with the ear not detecting changes of the phase angle of harmonics. The other is to do with why the brain doesn’t cancel two sounds when one is a polarity inversion of the other. That’s the real puzzle.

P.s. I found this article about Ohm, Helmholz and Seebeck, which you need a science background to understand. My brief conclusion after a partial read, is that if the amazing signal processing abilities of the brain were realised at the time, there would have been more agreement between them. It’s the brain that creates sound, using information supplied by the ears. https://www.journals.uchicago.edu/doi/full/10.1086/710318

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    I don't know enough about this as 'science', to provide an answer [other than knowing that phase-shift is part of how you know where a sound comes from - Haas effect & all that] but this says Ohm had to give up on that idea - en.wikipedia.org/wiki/August_Seebeck
    – Tetsujin
    Jun 25, 2021 at 10:55
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    I had to look up polarity. Maybe someone else will find this helpful: Polarity is a function of positive and negative wiring, while phase is a function of time. Although, maybe that should be more generally "positive and negative inversion". Inversion has one result, phase time shift has infinite results.
    – Michael Curtis
    Jun 25, 2021 at 13:55
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    @ToddWilcox "Polarity inversion is similar to 180° change of phase, but they are technically not the same." – Are you sure about that? Suppose that sound A is sin(x). Then suppose that you create sound B by inverting the polarity of sound A, meaning that sound B is -sin(x). Then you create sound C by doing a 180° change of phase on sound A, so that sound C is sin(x - 180°). Well, -sin(x) is sin(x - 180°), so sound B is the same thing as sound C. So it seems to me like polarity inversion is the same thing as a 180° change of phase.
    – Tanner Swett
    Jun 25, 2021 at 14:11
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    Regarding your last paragraph of the update - when you use headphones, you separate the brain's processing from the acoustics of the room (present when using speakers). You've discovered that the brain does not sum the two signals from each ear. It decodes them separately and then creates a sense of space (as best it can) based on correlation or decorrelation between the two signals. If you want to test phase sensitivity in human hearing to verify Ohm, the only scientific way is to alter the phases of two signals presented to one ear only.
    – Todd Wilcox
    Jun 25, 2021 at 14:43
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    @ToddWilcox I think the same goes for finite-time sounds, though. You can take any real-life sound and approximate it arbitrarily well as a sum of lots of sine waves of various frequencies. Then, if you phase-shift all those sine waves by 180°, the result is the polarity inversion of the original sound. That said, I admit that if you have a sound which just consists of a single pulse (an increase in pressure followed by a decrease in pressure), it's not really clear that the idea of "phase-shift that pulse by 180°" really makes sense.
    – Tanner Swett
    Jun 25, 2021 at 15:04

4 Answers 4

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You don't notice the phase of a particular note that arrives in one ear. But the brain can detect phase differences between your ears. That's the main mehod your brain uses to work out which direction a sound is coming from. If a sound is coming from the left, it will arrive earlier in the left ear than the right, and there will be a phase difference.

Inverting the polarity of one stereo channel gives the brain no way to work out where the sound is coming from, which is why it can sound odd. To me, it sounds strangely hollow.

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    It comes from 'everywhere except where it could' so your brain turns to mush trying to work it out. It's physically impossible in real life, so you cannot work it out.
    – Tetsujin
    Jun 25, 2021 at 12:40
  • Todd and Simon, isn’t it time difference or delay that the ear detects and uses for location. I’m now reluctant to use phase delay because of different interpretations :-) I’m an electrical engineer.
    – Brian F
    Jun 25, 2021 at 14:25
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    @BrianF As an EE, I think you have a leg up on audio engineering and acoustics, but there are some important differences. First, I suggest letting go of the steady state when it comes to audio. Even though the time scales can be very long relative to the wavelengths, considering audio (in electrical or acoustic form) as transient is helpful in distinguishing idealized theory from practical understanding. Also, our ears are not scientific devices, so at least a bit of research into auditory anatomy and psychoacoustics might help a lot.
    – Todd Wilcox
    Jun 25, 2021 at 14:39
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    Do you have sources/references for this?
    – Mateen Ulhaq
    Jun 26, 2021 at 5:17
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    When you say "it sounds strangely hollow," do you mean hollow in a metaphorical sense, meaning it sounds empty and has no substance? Or do you mean that it sounds like something that you might hear while standing in a hollow tunnel and the sounds are echoing all around the walls and you can't tell where they are coming from?
    – Ben Miller
    Jun 26, 2021 at 13:24
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I used to be a sensory neuroscientist, and I teach systems physiology. The ear is phase sensitive at low frequency, which is why inter aural time delay is the dominant mode of horizontal auditory localization at low frequency. Hair cell dynamics are too slow for phase sensitivity at high frequency, where interaural intensity differences, caused by the head's acoustic shadow, dominate localization.

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    I agree, the ear is phase delay sensitive, meaning the timing delay between wave fronts. Ohm was really considering the effect of shifting the phase angle of a harmonic sine wave. I think these different interpretations have caused some confusion. I still have some confusion, but putting it down to the fact that no-one really knows how the brain analyses sound waves, or do they?
    – Brian F
    Jun 26, 2021 at 11:25
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The ears, and our neuro processing, are amazing gadgets. Yes, the phase difference between left and right contributes to directional location, but there's more than that going on. If that were the only difference, we couldn't tell , say, 30 degrees left - front from 30 degrees left- rear.
Each ear - the external part, has all sorts of ridges and stuff that lead to an incoming wavefront generating phase-shifted echoes. The phases of these echos vary depending on where in the hemisphere the sound originated. The brain then "analyzes" the whole shebang to locate the source. This is in addition to the left vs. right processing. Try these two experiments (which have been done in controlled lab settings:

  1. completely block one ear. You'll still get a pretty decent idea of the direction a sound is coming from.
  2. now "fill in" the other external ear with putty so it's a blank smooth surface. Now you lose almost all directional information.
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  • Very interesting. I’m concluding that the brain is an amazing gadget, and that “sound” is generated by the brain and not the ears. There’s some amazing signal processing going on there. Another puzzle is why I’m gradually losing my sense of pitch, along with my hearing - a real bugger. I blame the ear for that, and might have to switch to percussion.
    – Brian F
    Jun 25, 2021 at 16:52
  • This article is interesting. If the cilia change length with hearing loss, that could be why my sense of pitch is slightly different between my 2 ears. sciencedaily.com/releases/2012/10/121002113414.htm
    – Brian F
    Jun 25, 2021 at 17:22
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    @BrianF - I once had an ear infection for a week [during which I had to do live shows, bass & vocals] where one ear was quite clearly the best part of a semitone out from the other. I knew which was "correct" but by heck it was a tough couple of gigs, trying to ignore the "wrong" one. Intellectually, I knew which was which, but my internal 'brain tuner' believed both, equally.
    – Tetsujin
    Jun 25, 2021 at 17:28
  • Is putting putty in your ear really advisable?
    – user253751
    Jun 25, 2021 at 21:30
  • The putty thing will impact vertical localization of sound, but not horizontal. Horizontal localization is poor with one ear, always.
    – Scott Seidman
    Jun 26, 2021 at 1:43
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Audiophiles sometimes claim that absolute polarity can be detected - that a bass drum note sounds different whether the initial transient is a pressure wave 'blow' or 'suck'. But audiophiles claim all kinds of peculiar things. Prepare to be amazed at the products on sale here!

https://www.russandrews.com/

However, as you say, RELATIVE polarity can certainly be detected. It may not matter with which polarity the two sides of a headset or a pair of speakers are connected, but it needs to be the SAME polarity.

As to cancellation - yes, if two speakers, in a perfect room, fed opposite polarity audio to a one-eared listener, you'd get perfect cancellation. In practice, the result is reduced bass. The pragmatic test for (stereo) speaker polarity is to place the two speakers side by side and play a mono signal. Swap the wires on one speaker. Whichever way gives most bass is right. (Well, maybe not right if you believe in perception of absolute priority, but they'll both be the SAME polarity.)

Isolated separate feeds to each ear are another matter completely. The brain makes some sense out of it, but not always in a predictable way. You can create some interesting 'unreal' effects.

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    What's the purpose of the link to a shopping website in the middle of this answer?
    – Tanner Swett
    Jun 25, 2021 at 14:13
  • To illustrate the gullibility of some audiophiles.
    – Laurence
    Jun 25, 2021 at 15:34
  • but it doesn't… it's just a shopfront.
    – Tetsujin
    Jun 25, 2021 at 15:53
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    A couple of actual examples might have been amusing. A storefront is just three clicks past being bothered.
    – Tetsujin
    Jun 25, 2021 at 17:07
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    I guess I didn't know what I was supposed to click on after clicking that link. I was expecting some kind of essay or blog or something and was a little confused to see a shopfront. But I'm having a thick-headed day today, so maybe it's my fault. :D I probably would have gotten the point immediately if you'd written "Look at some of the products on this website and prepare to be amazed!"
    – Tanner Swett
    Jun 25, 2021 at 19:14

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