I know mostly how speakers work, but how can they generate more than one frequency/amplitude at once?

Answer 1

Speakers don't generate any frequency.
Speakers REPRODUCE the input sound signal, which by itself consist of multiple frequencies.

For example: say they need to reproduce a certain sound S(t) (where t is time), one can express that signal as a series of sinusoids; say S(t) = a_1 cos(w1*t) + a_2 cos(w2*t) + ... + a_n cos(wn*t).

a_1 to a_n are the different amplitudes of the sinusoids
w1, w2, ... wn are the frequencies

So, any signal can be expressed as a sum of sinusoids. This is called the frequency response of the signal.

Answer 2

A pure tone is simply a cycle of energy, going from minimum through maximum, back to minimum again. The speaker cone does the same thing; the electrical signal causes the cone to push outward to maximum, then back inward to minimum, etc.

Most sounds, though, are not pure tones, but a combination of tones which creates distortions of sorts. Real world noises combine to push through the air and, although your ear can distinguish various attributes within, it still only receives the combined information. (Sort of 'encoded' sound waves.) The electrical signal is the same, and causes the cone to pause, then continue, to retreat, in a similar fashion to the original combined frequencies, which recreates it again.

Some signals are just too far apart for a single speaker to accurately reproduce ALL the frequencies. For this reason, good speaker systems incorporate filters to separate the long-moving low frequencies (which require large cones), the faster-moving mid-range (which require smaller cones), and the very short high frequencies (which are better reproduced using horn technology).

A very simplistic explanation and not entirely accurate as there is much more to sound and audio, but suffices for a most basic description.