Feynman claimed "The ear is not very sensitive to the relative phases of the harmonics." Is that true?

Question

In The Feynman Lectures on Physics, Dr. Richard Feynman claimed that the ear (I assume he meant the human ear) is not sensitive to the relative phases of harmonics.

However, I was asked to test electronic filters with a Textronix Vista tester using an impulse which is a pulse that is infinitely narrow, and of course is limited in its peak voltage by the filter's maximum input voltage. While an impulse does contain all harmonics at the same amplitude as the fundamental, making it perfect for testing a filter, the impulse, being very narrow contains virtually no energy, so the amplitudes of everything from the fundamental to the thousandth harmonic are very, very small in amplitude and any noise in the system overwhelms the signal making it impossible to get a stable and consistent reading of the filer's cutoff frequency.

I took the spectrum of an impulse, randomized the phases of all harmonics, performed an inverse FFT and normalized the time domain wave to fit the filter's maximum input voltage. This technique worked wonderfully and gave me stable, repeatable results. I published this technique on using white noise to test a filter.

Because white noise is spectrally identical to an impulse, but the phases of the harmonics are different, this seems to prove Feynman's statement on the phases of harmonics wrong. Did I outsmart Feynman?

Answer 1

What Feynman means by that statement is that the "ear" (cochlea) is a spectrum analyzer with a large set of very narrow band filters each followed by a square law (energy) detector, that is all. You can test if Feynman is correct in saying that the phase has no importance by having two tones of equal frequency and amplitude, one on the left ear and one on the right ear simultaneously, meanwhile varying the relative phase between them. Experiments have shown that the brain cannot tell their relative phase variation.

Then how does a human tell the direction of the wavefront, ie., direction from which the sound originates? By measuring a time difference of arrival between the two ears. Radar/sonar prefer phase measurements when is available because it is more accurate in white additive normal thermal noise. But in a complicated multipath environment (echo) such as almost all ground acoustic environments are the real life performance between phase coherent and time difference of arrival (TDA)* measurements can actually prefer the much simpler TDA unless rather complicated interference removal algorithms are employed in the phase difference measurement.

The same indifference to phase happens when measuring on one ear one frequency and on the other a harmonic of the same frequency. The brain cannot discern the phase of one relative to the other although the relative phase between them is meaningful for they are coherent signals. This is because both are detected noncoherently.

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• TDA of PDA because the ears are spatially separated by the skull therefore both the relative phase and the relative arrival time depend on the direction of the acoustic wavefront.

Answer 2

No. You just found a special case where the relatives phases of all the harmonics adds up into such a big difference in the waveform that you actually can hear it. I expect it works if the fundamental frequency is low enough for you to hear individual clicks with silence in between. At higher fundamental frequencies, you would not be able to distinguish delta functions from white noise, unless the impulses were loud enough to damage your eardrum.

Hearing works by different frequencies stimulating different receptors in the ear. You hear a pitch if a receptor is stimulated, regardless of phase.

Answer 3

The way hearing works is that acoustic vibrations that reach you inner ear cause mechanical vibrations of the so-called hair cells inside cochlea. Different hair cells happen to have different sizes and hence different natural vibration frequencies. as a result they only respond to a narrow frequency range of external vibrations near corresponding resonant frequencies (the Q-factors of hair cells must be reasonable). What each such cell then transmits to the brain is the amplitude of its vibration. So in essence the ear works as a spectrum analyzer, but what reaches the brain is the intensity of each harmonic, not its phase. To summarize, what Feynman says here sounds right to me.

Answer 4

We can show his claim to be false even more simply: imagine one drummer drumming at 60 bpm, and another drumming at 120 bpm. Would the human ear be insensitive to their relative phases? Of course not! So clearly Feynman's claim is true only for sufficiently high frequencies. How much is "sufficiently high"? Somewhere in the neighborhood of 20 Hz. Below that, periodic signals are perceived as beats, and above that, they are perceived as tones. The human ear is sensitive to difference in beat phases, but not in tone phases.

As for your reference to the "fundamental frequency", I'm unclear what that's referring to. If we're talking about a theoretical ideal impulse, being infinitely narrow in the time domain means being infinitely wide in the frequency domain, so how can there be a finite fundamental frequency?

Of course, a true impulse is physically impossible; the infinite narrowness marks it as nonphysical. What's not as obvious is that true white noise is also impossible; as you note, white noise has the same spectrum as an impulse, so its spectrum is also infinite. So if you have one signal somehow approximating an impulse, and another approximating white noise, that raises the question of just what you consider to be "close enough" to the theoretical ideal for it to bring Feynman's claim into question, and what bandwidth your approximations have. If you're dealing with less than 20 Hz, then we're into beat frequency, and if it's higher than 20 Hz, then it must last less than 100 ms.

Answer 5

There is a mathematical catch in the example of white noise and impulse. The two are spectrally identical only when considered as infinite signals in time. Human ears clearly analyze sounds only locally in time: they are not really mathematically perfect spectrum analyzers, which you can model using the Fourier transform. They are like real-world spectrum analyzers, so they measure things locally in time: the mathematical analogue of the Fourier transform in this case is the FBI transform, which multiplies the signal by a Gaussian cutoff localized in time before measuring the frequencies.

The point is that the Fourier transform of white noise and impulses are identical in absolute value, but their FBI transforms are not :)

That is why human ears can tell the difference between the two. They are real-world spectral analyzers, not mathematically perfect ones. Whether this '''''proves''''' Feynmann wrong or not it's a matter of interpretation (I personally don't fully understand his sentence). What I want to underline is that one should be very careful when talking about frequencies and spectrum: real-world applications want to measure spectral information only locally in time, but if you think of spectra mathematically, they only make sense when you look at signals that are defined for all times.

Answer 6

Your question is a very long-winded way to present the following simple idea: "if the human ear does not distinguish between two waveforms whose spectral compositions are identical, but whose components' phases differ, then why does white noise sound different from an impulse?"

This is actually quite an interesting question. I cannot comment on Feynman's original intent, but it is very well established that altering the relative phase between two audible sounds and listening to their superposition will lead to dramatically different results for different relative phase offsets.

I present two examples: one mathematical and one pratical.

• Consider a single sine wave. If I were to duplicate it and listen to the superposition of the duplicate with the original, then I would hear a louder sine wave. If I were to shift the phase by 180°, I would hear nothing. Thus, I am sensitive to the relative phase.
• While recording music in professional studios, a significant challenge is to ensure that when you record an instrument with two microphones, both microphones are equidistant from the source, and are thus "in-phase." Should the differences be unequal, there will be destructive interference between the two microphones' signals if you listen to them simultaneously, which has a distinctly noticeable weak sound, and often a kind of artificial "swirling" sensation too.

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I would, however, strongly encourage you to be respectful, both to people here and to scientists of the past who cannot respond to defend their opinions. Asserting that someone is wrong does not mean you "outsmarted" them. If someone in the comments claims they disagree with someone else, they are not claiming to be "smarter." This is the internet and we're just here to learn and have fun, not to assert superiority and gain fame. There's no need to speculate about whether people who reply are speaking from experience, or to suggest that they don't know about FFTs. Tell them which part of their argument you disagree with, or move on.

Answer 7

Let's focus on just one ear because with two ears things get much more intricate. Let's take a waveform having a frequency e.g. 500Hz, and a waveform having a multiple of it e.g. 1000Hz. By creating by computer these waveforms you may shift the phase highest frequency from e.g. 0 to 360 degrees.By testing it if you feel the same sound when the phase is shifted than the assumption is true, if these are different sounds the assumption is false. I indicate to use submultiple frequencies, because if frequencies are non exact ratios, then the reasoning is different. TO BE NOTED THAT if superimposed frequencies are very near, then when they are in phase you hear loud, when when they are in opposite phase then you don't hear anything (supposing to have them of the same amplitude). So if the phase shift is so small you may hear for a very long time a very loud sound at the common frequency but that sound is modulated by another frequency as these fell slowly out of synchronization up to arriving to total silence where one cancels out the other. So generally speaking the statement is theoretically wrong as the phase shift in that case may be detected (but at out of sound bands). For sub multiple frequencies it may by true under experimental proof!!! ( I suppose it is true -- but I haven experimented yet ) , BUT YOU MAY JUST HIT TWO notes on the piano, at once ( it is never at once any way so phases will be out of phase but these will also be not exactly multiples) if you hear every time the same sound then the statement is practically true !!!!!! I actually don't have a piano at hand, but musicians do not change music when hitting one note 0.00001 second before the other note !!!!!! so we may assume from third party experience that it is true !!!

The previous phrase seems to be wrong after experimental test. I used the site https://meettechniek.info/additional/additive-synthesis.html and created a sound with a frequency and it's second degree harmonic, by changing the relative phase it seems to my hear that something is detected. BUT PAY ATTENTION if frequencies are not exactly submultiples (as e.g. in the piano) there is no phase shift as that is continuous, and thus the difference cannot be detected. Please check with your ear and revert back !!!

Answer 8

Feynman is talking about "harmonics" in that sentence. "Harmonics" is used in the context of periodic signals. Concerning periodic signals, the human ear has a frequency range that goes from 20Hz to 20.000Hz.

If you really wanted to disprove what Feynmann is saying, you should consider a periodic pulse signal of frequency that sits comfortably between 20Hz and 20.000Hz and compare it with a periodic white noise. And clearly you want the two signals to have the same volume, so you would have to run the periodic pulse on a device with a large voltage output so that the pulses are as close as possible to ideal ones.

If you did the above experiment and found a clear difference between the two sounds, maybe you would convince me.

Answer 9

A video containing two identical sounds, identical spectrally, but not in the phases of the spectra, proving that humans can hear the relative phases of harmonics.