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They don't produce multiple frequencies at the same time, they reproduce a representation of multiple frequencies at any point in time.
Suppose a driver is called on to reproduce a combination of 20 hz and 800 hz tones. To see how it works, first we have to separate the tones.
With just a 20 hz tone, the driver moves back and forth 20 times a second or full forward and full backward in 50 milliseconds. The driver will move to its full forward position in 12.5 milliseconds. The air in front of the driver is compressed.
With just the 800 hz tone, the driver will move full forwards and backwards 10 times in the same 12.5 milliseconds. The air in front of the driver is alternately compressed and rarefied.
For both tones, the driver will vibrate 10 times back and forth as it is moving forward in that 12.5 ms time frame. This causes the compressed air of the 20 hz tone to be superimposed with alternately compressed and rarefied air from the 800 hz tone which causes the ear to hear the combined tone.
What is happening is the 800 hz sine wave is "riding" the 20 hz sine wave, creating a combination sine wave. If you take an 800 hz sine wave and draw the zero axis in the shape of a 20 hz sine wave, that represents the speaker cone movement at any point in time.