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I inverted the waveform of a given song and was wondering what will happen.

The result is that it sounds the exact same way as before.

I used Audacity and doublechecked if the wave-form really is inverted.

The second thing I tried was:

I removed the right channel, duplicated the left one and set the duplicated layer as right channel. This way I made sure that both channels are exactly the same. Then I inverted the second channel only. I thought that this would create some kind of anti-noise, but it didn't.

Why is that?

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what is inversion for a waveform? – Yrogirg Sep 5 '12 at 13:46
Not really a physics question but one about the response of the human hearing apparatus and how the brain interprets the results. – dmckee Sep 5 '12 at 14:53
@dmckee that might be true as soon as you know the answer, but I didn't do that in the first place ;) – Sven Sep 5 '12 at 15:12
I'd say this is a physics question because the answer (as Emilio says) is that it's the power that matters and the power is the square of the amplitude. The ear is, after all, a mechanical system. – John Rennie Sep 5 '12 at 18:46
BTW, when a musician says "inverting a song," the meaning is turning the melodic line upside-down, not inverting the sound wave. – Ben Crowell Sep 29 '13 at 2:48
up vote 16 down vote accepted

The human ear responds only to the intensity $I$ of the sound it receives (more specifically, to the intensity distribution over the different frequencies) and this goes more or less like the square of the amplitude, $$I\sim A^2.$$ Changing the sign of the waveform changes the sign of $A$, which has no effect on $I$.

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The ear also responds to frequency, of course, but inversion doesn't affect that either. – dmckee Sep 5 '12 at 14:53
I've heard that the human ear actually can detect phase differences at very large amplitudes. E.g., you may be able to tell the difference between a cannon blast and the inverted version of it. – Ben Crowell Sep 29 '13 at 2:47
You can definitely hear phase differences at low frequencies. If you add up sine waves of frequency 10, 20, ..., 10000, each with the same amplitude and phase, it sounds like a series of clicks; but if you make the phases uncorrelated it sounds like a metallic hissing sound. This is only relative phase though - you won't hear the difference between and sound and its inverted version through this mechanism unless there is another sound playing at the same time. – Nathaniel Sep 29 '13 at 3:54
Anyone with the free SuperCollider audio programming language can hear this by comparing play{*10).mean} (same phases) to play{*10,{2pi.rand}!1000).mean} (randomised phases). Also note that the difference in sound is not due to phase cancellation, since each sine wave has a different frequency. – Nathaniel Sep 29 '13 at 3:56
@Nathaniel: Yeah, I think in your example you're seeing the fact that the ear-brain system is neither completely time-domain nor completely frequency-domain. – Ben Crowell Sep 29 '13 at 19:15

Re your last question: what you've achieved is essentially the same as if you wire one of your speakers the wrong way round so it moves in antiphase to the other speaker. In principle there will be points equidistant from both speakers where the sound waves cancel and you get a quiet spot. However as soon as you move closer to one speaker than the other you no longer get perfect calculation. Plus unless you're in an anechoic chamber you get sound reflections that mess up the cancellation. In practice it's very hard to get the sounds to cancel.

This principle is used in active noise control to reduce noise, but it does require very precise control of the sound phase and volume.

In the HiFi world connecting one speaker the wrong way round is something most of us have done at some time. It doesn't cancel the sound, but it does mess up the stereo imaging and make the whole thing sound rather muddy. This will be more pronounced the better the HiFi.

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I suspect the finite size of the speakers will also be enough to wash out any interference pattern in practical situations, though. – Emilio Pisanty Dec 10 '12 at 1:05
@EmilioPisanty: I think interference between stereo speakers can be important for low bass, since, e.g., many people can hear 30 Hz, which corresponds to a wavelength of 11 m. – Ben Crowell Sep 29 '13 at 19:17

Inverting a waveform is the same as rotating your speaker around 180 degrees to face away from you. (Yaw or pitch - not roll!)

The changes in air pressure your ear detects is exactly the same.

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