One way to look at it is the following :
In theory, ideally, you could use one single speaker on your hi-fi, just the way it’s done on a cheap radio.
However, you would face two problems if using one single speaker instead of a medium, plus a woofer plus a tweeter:
- Efficiency (bandwidth):
When you send an electric signal of a given frequency f to a speaker, it will vibrate to said frequency with an amplitude $A(f)$.
An ideal speaker would have a perfectly flat frequency response, i.e. $A(f)$ would not depend much upon f:
$A(f) = Constant$
However, in practice, said response is not a flat line, but a curve, centered around a given frequency. This is due to the fact that a speaker is a physical object, with a mass, a elasticity coefficient, etc, not unlike a bell or a guitar string.
A guitar string can be modeled formally as a harmonic oscillator. When you pluck it, it yields a given note, when you shorten it by putting a finger on a fret, it will yield a more high-pitched sound and so on. Thicker strings (more massive ones) will yield lower frequencies and so on.
One could in theory build a guitar with just one thick string, however but one would face the problem that it would be inefficient at yielding high pitched tones (unless you pinch so as to shorten it dramatically) and conversely, if it is a rather lightweight one, one would have to build a really ridiculously long guitar to yield the low notes.
The efficient solution for a guitar is to have a set of different strings, with different tensions and different masses.
For analogous reasons, a speaker with a certain mass, diameter, elasticity will be able to reproduce efficiently sound, as a (frequency dependent) response to the electrical signal which is send to it, in a limited frequency range.
Therefore to reproduce efficiently the whole spectrum of sound covering the range of human hearing, one uses a set of two or three or more loudspeakers whose natural frequency response curves overlap, so as to complement each other and cover the whole required range.
Just as when attempting to use a single guitar string to cover the whole range of the guitar (say: just using the low E string and pinch it really high to reach high pitched notes), one would face a quality problem on top of the aforementioned efficiency problem (very high pitched notes on a thick E string would be hard to distinguish), reproducing frequencies well beyond the efficient part of the frequency response of a speaker would not only require more energy, but it would not yield the same définition/clarity as adding a supplementary dedicated speaker (for a given frequency range).