Listen to these two sounds:
Is the second sound higher or lower than the first sound? (let us know in the comments). Play it again if you're not sure.
Ask a few other people to do the same. You'll find that some people hear the second note as higher and some hear it as lower!
(mini update: so far 5 commenters hear the second note as lower and 8 hear it as higher)
That's because it's an audio illusion. And just like an optical illusion an audio illusion can tell us something about the way we perceive the world around us.
The explanation is all to do with resonance and harmonics.
What is resonance?
When you pluck a guitar string the note it produces is the resonating frequency of the string. So you can think or resonance as the tendency of a system (like a tight string) to oscillate at a particular frequency when you put energy in it in the right way.
But it turns out that systems can have more than one resonating frequency. They can have a whole series of harmonics.
What are harmonics?
If you pluck that guitar string again but this time rest your finger gently on it right at the centre you'll hear a new note. This is also a resonating frequency of the string and it's twice as high as the first.
If you then rest one finger a third of the way down and another two thirds or the way down and pluck the string (with your third hand presumably) you'll get another resonating frequency. The pitch of this one will be three times that of the open string.
The points where you rest your fingers are called nodes. The places where, for that resonating frequency there is no movement. You could continue adding nodes and getting new frequencies along the way.
These are called harmonics. The first harmonic, or fundamental harmonic, is what you hear with an open string. The next one up is the second harmonic and so on. Here's what they look like:
Now in reality when you pluck an open string you're actually getting a mixture of all these harmonics but you only hear the fundamental. The other harmonics don't register as distinct notes but instead make the whole sound richer. Here's an illustration of the sound produced by a guitar string being plucked:
You only hear that lowest frequency but the other harmonics are there.
How does all this relate to the audio illusion?
Natural systems like the guitar string or human vocal cords tend to vibrate in this way, they vibrate at a fundamental harmonic and all the other harmonics on top. So our senses have evolved to interpret these mixtures of harmonics as a single tone coming from a single entity.
Here are two notes side by side:
As you can see the second note is lower. And this is exactly what you're hearing when you play the sounds at the top of this post except for one important difference. The fundamental frequency of the second note has been taken away so it looks like this:
That gap is "unnatural" and the way you interpret that depends on how your brain works.
It turns out that the way we perceive pitch isn't just to do with the tones we hear but also the pattern of tones. So for some of us our brains would receive the pattern of frequencies of the second note, ignore that fact that the pattern is broken, and interpret the sound as being lower. In other words your brain is hearing the fundamental harmonic that isn't there.
On the other hand, if you heard the pitch go up, that's because the pattern of frequencies is less important to your brain than the absolute lowest frequency.
Most people are a mixture of the two and depending on how you engineer the two sounds you can get anyone to hear or not hear the missing fundamental.
Did you hear it? Let us know in the comments.
You might also like the optical illusion in this post.
Update: Some interesting insight from Martin Coath who first told me about the effect: "The predisposition to hear one or the other is correlated with a volumetric asymmetry in Hesch'ls Gyrus - ie one of the auditory parts of your brain is bigger on the left or the right. (Schneider, Sluming et al Nature Neuroscience 8, 1241 - 1247, 2005)"
Another update: Awesome commenter sci ran my sounds through a frequency analyser and got this:
I've attempted to anotate this image to show what I think is going on (am I getting it right sci?):
So my original illustrations are a bit off. The sounds have fewer harmonics than I thought. But it does show the missing fundamental which I'm very excited about Thanks sci.