Simple experiments with beats and hearing

In the class I’m TAing, we are discussing beats. Beats are when you play two tones that are close to each other, but at slightly different frequencies. They will slowly drift from in phase to out of phase, like when your turn signal has slightly different timing from that of the car in front of you at a stop light. In sound, this results in the “wa-wa-wa” sound you hear when tuning two instruments to each other.

Beats depend on space as well as time. If two speakers play a tone, they can be in phase at one place and out of phase at another, since the distances to the speakers is different.  I had never actually played around with this with sound before, so I set up two speakers in a room where I could move both them and myself around pretty freely.

Making the speakers play the same pure tone (440 Hz), I found it was quite easy to observe the interference pattern of the speakers by moving my head around. And when the speakers were placed far enough apart, the phase difference could be quite different at opposite ears, so the sound would appear only in my left or only in my right ear. Also, by putting the speakers the right distance apart, I was able to observe turning the volume on the closer speaker up from zero and hearing the volume of the sound go down as the front speaker interferes with the back one. (It’s not practicable to make the sound seem to disappear entirely.)

Next, playing notes separated by 0.5 Hz, I found I could stand in one spot and hear the sound move from my left ear to my right ear and back again once every two seconds. This never sounded as if the source itself was moving around. Instead, the sound felt as if it was being played right next to my ear, even though the speakers were a couple meters in front of me.

These are just simple things, but still striking, since we rarely encounter coherent sound sources set up this way in daily life. Some time ago I did one other experiment accidentally that had an interesting result. I was listening to an app that creates beats by outputting different frequencies to the left and right audio channels, but I didn’t hear the beats. After a bit of confusion, I realized it was because I was wearing earbuds – there was no interference because nobody was getting both signals at once. Playing the tones through speakers instead, I heard the beats. However, when I turned the frequency down, I could hear the beats even with the earbuds. Somehow, your brain collects phase information about sound, but only if the sound is slow enough. The transition occurred somewhere around 600 Hz, or roughly a millisecond. This corresponds fairly well to the width of a nerve impulse, so a likely hypothesis is that you can only determine the arrival of the peak or trough of a wave to a time comparable to the width of a nerve impulse, which means you only have meaningful phase information down to around the 600 Hz I heard. (In a discrete Fourier transform, you have information about frequencies up to half the inverse of your sampling rate, so this checks out pretty well.)

The app I used was similar to this one, but I think my cheap headphones don’t process audio channels properly, as I can hear the beats even with one earbud in, both with that app and with WIkipedia’s file.

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