I was recently playing with this Wolfram Demonstrations applet, which demonstrates beats.

At first I thought the app didn't work because I couldn't hear any beats. Then I realized that the applet doesn't analytically add two sine waves of nearby frequencies and play the result; it plays different sine waves to the left and right audio channels. Since I had headphones on, I only heard one frequency per ear, and only consciously detected a single tone. When I took the headphones off and held the ear buds close together, I could hear the beats distinctly.

Messing around a little more, I found that when I lower the frequency to around 600 Hz or lower, I begin to be able to hear the beats even with headphones on.

What's happening? Are my ears for some reason picking up relative phase information only at lower frequencies? Are only lower frequencies transmitted effectively through my skull?

I would guess it's a coincidence that I begin to hear beats when the wavelength of the sound (in air) is on the order of the distance between my ears, but is that right?

  • $\begingroup$ Note the similarity between the wavelength at 600 Hz and the size of your head. I'm not sure what that means, but it may not be a coincidence. $\endgroup$ Commented Sep 24, 2011 at 15:42
  • $\begingroup$ @dmckee Yes, that was in the question. $\endgroup$ Commented Sep 24, 2011 at 15:45
  • $\begingroup$ Well, I feel stupid now. $\endgroup$ Commented Sep 24, 2011 at 15:51
  • $\begingroup$ I wasn't specific earlier because I don't have a reference, just a vague memory of someone telling me, but I believe that localization by phase difference because possible when the separation becomes shorter (but not $\ll$) than the wavelength, which offers a reason why it would be advantageous to be sensitive to phase differences at low frequency. $\endgroup$ Commented Sep 24, 2011 at 16:01

1 Answer 1


The beats are audible at lower frequencies because your ears do in fact pick up phase information, but only at these lower frequencies.

When a sound enters our ear, we magnify it via mechanical oscillations of bones and hydraulic effects, ultimately causing vibration in a thin film in our inner ear called the basilar membrane. Different sections of the basilar membrane will vibrate in response to different tones. The basilar membrane is connected to thousands of small hairs, themselves connected to mechanically-sensitive ion gates. Oscillations of these hair then trigger the ion gates. The ion gates send electrical impulses down neurons to our brains.

Empirically, it is observed that these nerve impulses almost always begin at the peak amplitude of a vibration of the basilar membrane. Thus, if our two ears receive sound with different phase, they will fire nerve impulses at different times, and our brains will have access to phase information.

An interesting demonstration of this was given by Lord Raleigh in 1907. He theorized that phase difference detection between the ears was a key component to our ability to localize sound. When Raleigh played two tuning forks that were slightly out of tune, so that the phase oscillated, his found that human perception of the location of the sound oscillated from the left to the right of the listener's head.

At high frequencies, we lose phase information. This is because of uncertainties in the exact time of arrival of a nerve impulse. A typical nerve impulse lasts several milliseconds, so above 1000 Hz the uncertainty in arrival time becomes comparable to the frequency itself, meaning we lose phase information. It turns out that we mostly lose the ability to localize sound in the range 1000 - 3000 Hz. Above 3000 Hz, different physiological mechanisms related to the "shadow" of your head allow us to localize sound again.



The information about Rayleigh's experiment and firing at the peak of oscillations is from chapter 5 of "The Science of Sound" by Rossing, Wheeler, and Moore.


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