So, I'm no expert but I read about this some years back in a fascinating book called How Music Works (not David Byrne's), and it explained how sounds of a given fundamental frequency (its first harmonic, the frequency we would use to identify a particular note), will be recognized by our brain as the fundamental frequency, even if only the other harmonics are present, while the first is missing, which can allow small speakers with poor ability to reproduce low frequency sounds, to reproduce a low note without actually needing to reproduce the fundamental frequency.
The book uses A2 as an example because its fundamental frequency is 110Hz and it's a nice easy number. That makes its second harmonic 220Hz, and its third 330Hz, etc. And in a normal note, we hear all of these harmonics at once but in a way that repeats at 110Hz, so we can always identify it as that fundamental frequency.
Let me quote some of this before I completely mangle the explanation:
All these vibrations (with lots of others) happen at the same time, as a complex dance which repeats a whole cycle at the lowest frequency involved – 110Hz.
Some of this is also explained on wikipedia
Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series.
The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player.
So more from the book as to how this relates to the question at hand:
Look at this collection of frequencies. Together they make up our old
friend the note A2, which has a fundamental frequency of 110Hz:
110Hz, 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz etc.
As you know, the timbre of an instrument is made up of the various loudnesses of these ingredients within the ripple shape. Whatever the mixture of ingredients, our brain recognizes this as a note with an overall frequency of 110Hz. Even if the loudest, strongest component was 330Hz, the overall pattern would only be completing its dance 110 times a second – so the fundamental frequency is 110Hz.
Rather than just being a minor contributor to the sound it is possible that one of the harmonics could be completely silent. If, for example, the 770Hz frequency was completely absent, we would still hear the remaining harmonics as part of a note which has a fundamental frequency of 110Hz. This is because only 110Hz can be the head of a family which includes 110Hz, 220Hz, 330Hz etc. We could have several of the harmonics silent – and still the fundamental frequency would be 110Hz.
Now the odd bit: we can even remove the first harmonic, the fundamental – 110Hz – and the fundamental pitch of the note we hear would still be 110Hz. This sounds a little insane but it’s perfectly true. If you hear the following collection of frequencies: 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz etc. you will hear it as a note with a fundamental frequency of 110Hz, even though the sound does not contain that frequency.
And bringing it together:
Nowadays it is possible to get ridiculously low frequencies out of small speakers by utilizing the ‘missing fundamental’ idea. Let’s say your speaker won’t do much at frequencies of less than 90Hz, but you want to hear the note A1 clearly – and it has a frequency of 55Hz. If you feed the harmonics of 55Hz to your speaker without the fundamental (i.e. 110Hz, 165Hz, 220Hz, 275Hz) you will hear 55Hz loud and clear even though the lowest frequency at which your speaker is moving is 110Hz.