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one type i know is based on piezo electric effect
a piece of quartz under mechanical pressure along one of its axes generates a small dc voltage, its amount proportionally with the pressure.
another type may be based on a "dynamic loadspeaker" like piece.
acting on the membran with some pressure (not only acoustic but mechnical too) may develop a magnetic field.
this last type isnt always proportinal with the stimulus.
Most of them have an elastic membrane, wich deforms under pressure. Attached to the membrane is a so-called strain-gage, essentially a Wheatstone bridge whose resistors are "stretched" when the membrane gets distorted. The stretching makes the length of the resistors increase and so does their resistance. The output of the bridge (in the mV range) is them amplified and used to measure the pressure. Temperature compensation is usually necessary, since the resistors in the bridge depend on temperature, too. Therefore, the sensor includes frequently a temperature sensor, whose output is used to compensate the bridge's reading.
"Intelligent" sensors use a microcontroller to do linearization and temperature compensation. Linearization is necessary since most of the above elements are non-linear.
Modern sensors use semiconductors for the strain-gage, but the principle is very similar.