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In order to register all of the minute pressure fluctuations in a sound wave, the microphone diaphragm has to be extremely sensitive. This means it is very thin and moves only a short distance. Consequently, the microphone produces a fairly small electrical current.
This is fine for most of the stages in the process -- it's strong enough for use in the recorder, for example, and it is easily transmitted through wires. But the final step in the process -- pushing the speaker cone back and forth -- is more difficult. To do this, you need to boost the audio signal so it has a larger current while preserving the same pattern of charge fluctuation.
This is the job of the amplifier. It simply produces a more powerful version of the audio signal.
The pre-amplifier works the same basic way as the amplifier: The input circuit applies varying resistance to an output circuit generated by the power supply. Some amplifier systems use several pre-amplifiers to gradually build up to a high-voltage output signal.