You're hearing the overtones, the harmonics that make the signal sound different to just a pure sine wave.
The human brain is very good at filling in the missing information based on that. You'd still notice a massive difference if your speakers could do 40Hz though.
To add to this, it's part of what makes a bass guitar sound different from a clarinet, flute, saxophone, distorted guitar, etc...
The fundamental pitch is the lowest frequency in this collection of harmonics/overtones.
A really neat (or kind of neat) demonstration is to sit at a pipe organ (you know we all have one of those in the attic someplace :P ) and you can start with a pure-ish tone, and add sounds to it. Some of them you actually end up adding different notes (like a 3rd and a 5th) to the original note. So you play a single key and you kind of end up with a major chord, but after you start playing a melody or chords with it (multiple keys pressed), the brain kind of recognizes it as a single note, and not a collection of notes.
They mess around with this when comparing digital to tube distortion also I think. I read an article a long time ago comparing how certain harmonics are weaker or stronger (unless you go out of your way to tweak them) with you use digital or solid state distortion as opposed to tube distortion, and this is part of the difference in sound.
There are something like 11 or 12 harmonics that we are capable of hearing that can be added or subtracted from any fundamental pitch to make an instrument sound like a clarinet, or a buzzy distorted guitar (or saw wavey like a saxophone).
Interesting stuff actually.
We did the pipe organ thing in one my music classes in college.
And to bring it back to the point I quoted above, I think that is correct, that you can have all of the harmonics (because they follow the Harmonic Series, a good thing to look up, same thing as if you play harmonics up any particular string heading toward the nut), and if you play the correct harmonics for a particular fundamental tone, you can actually remove the fundamental pitch and your brain will still know what note it's supposed to be. Hence playing open E on a bass guitar through 60Hz minimum speakers, and still knowing it's a low E, even though the speakers probably can't produce that note, or not very strongly.
These would be the actual sounding harmonics for the lowest C that is notated:
It's a little tough to explain (for me at least), but easier to demonstrate.