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Briefly, a headphone or loudspeaker consists of a coil (solenoid) fixed to a diaphragm (in the case of headphone) or a paper cone (in the case of a loudspeaker). The coil is placed in a static magnetic field provided by a permanent magnet.
When electrical signals of audio frequency are fed into the coil, the signal current in the static field will produce a force pushing or pulling the diaphragm or paper cone. With the variation of the intensity and direction of the signal current, the diaphragm or paper cone is set into rapid vibration in line with the audio signal frequency. The vibrations cause air in front of the diaphragm or paper cone to vibrate, thus producing the desired sound waves.