| The first thing to keep in mind is that a speaker doesn't vibrate like a string does; since it moves under its own power it can move almost instantly to any position it wants to. It can dance however it likes, rather than just oscillating. Usually we make them oscillate because sound is what we're after, but we do have more control.
The second thing is that sound is just changes in air pressure (at a specific location) over time. If you were to measure the air pressure in one spot a few thousand times a second you would have a complete recording of whatever sounds occurred during that time.* That's very important: to record a sound you don't need to know anything but what the air pressure was at each point in time.
Since all we are doing is measuring the air pressure, what happens when we start to play another note? Just like the first note, it will create a pattern of increasing and decreasing air pressure over time. When you record, you won't discern any individual waves -- you'll just get the combination of the two. The current pressure of the first note plus the current pressure of the second.** If you were to graph your measurements you would get a funny looking wavy line representing the measured air pressure at each point in time.
All a loudspeaker needs to do to make sound is recreate the sound pressures you've recorded (or which you are playing through it). Since speakers can move however you like, you just cycle through the pressure levels you've recorded, moving the speaker back and forth to recreate the air's original movements.
As applied to bass guitar amplification, the speaker just attempts to recreate the string's movements over the pickup.
* "A few thousand" wouldn't actually sound so good. 44 thousand samples per second or so is the minimum for crystal-clear recording.
** If you've taken some math you can think of this as adding f(t)+g(t) for some notes f and g and time t.
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--Paul Donnelly
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