Well, it is connected to a pretty sophisticated computer. And, of course, we don’t really know for sure just how faithful our hearing does reproduce.
A paper cone by itself doesn’t make a very good sound reproducer. If you remove a cone driver from a speaker cabinet and connect it to a stereo, it won’t sound very good. The sound will have a very constrained frequency response (for one thing). Also, good speakers have more than one driver, as a single cone can’t reproduce all frequencies equally well (smaller cones are better for higher frequencies, and bigger cones are better for lower frequencies). All the parts of a speaker contribute to its ability to reproduce sound accurately: the various drivers, the cabinet, the electronics, etc. Audio engineers have been working for decades on ways to make speakers sound good, and the technology is sophisticated. We’ve come a long way from the early days of sound reproduction, when the speaker on a mechanical phonograph consisted of a vibrating membrane at one end of a metal horn. So it’s not really true that a paper cone can mimic virtually every sound (at least, not well). What’s true is that a full speaker system consisting of paper cones (and other types of drivers), a well-designed cabinet and electronics can mimic virtually every sound.
It’s important to realize that your brain does a lot to interpret sounds. When you hear several instruments playing at the same time, your ear receives a single sound wave that consists of the sounds of the instruments mixed together. The reason it sounds like several instruments to you is that your brain interprets this single wave into components. This is similar to what happens with vision - your eye receives a bunch of light focused on your retina, and your brain interprets this into objects, distances, etc.
Part of the quality of reproduction is due to speaker size. Big old woofers (deep base)and little tiny tweeters(high notes).
In the olden days many radio speakers has tears repaired with airplane cement and kleenex. Didn’t really notice much difference in sound quality.
Sorry, didn’t mean to geek out on you, there, but I’m very excited about the research whose announcement I linked to.
A steady tone from any instrument is a repeated pattern of air compression and rarefaction (the opposite of compression). What needs to be clear with regard to your OP is that the sound you get from the loudspeaker is not meant to be dependent on the natural resonant qualities of the paper cone. The paper cone is simply a tool to push air molecules around that is also light enough to be moved easily by the electromagnet at its center. Any resonant properties of the cone that may emphasize one part of the frequency range over another have to be compensated for by some other design feature of the speaker so the response is as “flat” as it can be across the entire audible sound spectrum, that is, all frequencies geting more or less equally reproduced.
Now as far as timbre, think of the paper cone being moved back and forth. You could move it really quickly in one direction and slowly back, or move it quickly in both directions but have it linger for a time at either extreme position, or have it move more or less evenly back and forth with a smooth change of direction, or any pattern you can think of. Each different type of pattern will give the sound a different tone quality, or timbre.
All of these timbres could be also be reproduced by playing a sine, or sinus wave (a simple pure tone) at several specific frequencies at specific volumes
Actually, speakers as well as most of the components from the mics to the amps are usually designed to give a response which is not flat. The speaker design differences then give the various speakers their own distinct sound.
True, but deviations are kept to a reasonable minimum. If a loudspeaker has noticably too much or too little treble or bass, we move, in the ears of the listener, from “distinctive” to “defective”.
I am going to be surgically fitted with eardrums that are 18", 6", and 1". 
Boy, are YOU gonna look funny.
Here’s another way to think about it: suppose you replaced a speaker’s paper cone with a violin. You would have a peculiar speaker which, if hooked up to a stereo, would produce non-violin sounds. It wouldn’t be a good speaker - I’m sure it would sound muffled and distorted. Still, it wouldn’t make a piano recording sound like a violin recording - it would sound like a piano recording played through a really bad speaker. Even a violin recording would probably sound bad.